Recent CCRMA Research in Digital Audio Synthesis...
Transcript of Recent CCRMA Research in Digital Audio Synthesis...
![Page 1: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/1.jpg)
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 1 / 54
Recent CCRMA Research in Digital Audio Synthesis, Processing, andEffects
Julius O. Smith IIICCRMA, Stanford University
DAFx-09, Keynote III, Como, Italy
September 4, 2009
![Page 2: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/2.jpg)
Overview
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 2 / 54
![Page 3: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/3.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 4: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/4.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 5: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/5.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 6: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/6.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 7: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/7.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 8: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/8.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 9: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/9.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 10: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/10.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 11: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/11.jpg)
Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 3 / 54
In my DAFx06 review, we looked at
• Early digital audio effects (delay lines, scanner vibrato, . . . )• Acoustic propagation models• Digital waveguide models (voice, strings, woodwinds, . . . )• Commuted synthesis (acoustic guitar, harpsichord, piano, . . . )• All my best accumulated sound examples!• That presentation is available online:
http://ccrma.stanford.edu/~jos/pdf/DAFx06KeynoteII.pdf
(sound examples via HTTP)What can I talk about now?New research results in the past three years?
![Page 12: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/12.jpg)
Since Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 4 / 54
Problem:
I haven’t done that much in the past three years!
Solution:
Summarize recent DAFx-related research at CCRMAas a whole
• Talk Design:
◦ New results in the past year (three years is too much)◦ Developed at CCRMA◦ JOS involved as collaborator or adviser
(i.e., I know something about it!)
![Page 13: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/13.jpg)
Since Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 4 / 54
Problem:
I haven’t done that much in the past three years!
Solution:
Summarize recent DAFx-related research at CCRMAas a whole
• Talk Design:
◦ New results in the past year (three years is too much)◦ Developed at CCRMA◦ JOS involved as collaborator or adviser
(i.e., I know something about it!)
![Page 14: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/14.jpg)
Since Three Years Ago
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 4 / 54
Problem:
I haven’t done that much in the past three years!
Solution:
Summarize recent DAFx-related research at CCRMAas a whole
• Talk Design:
◦ New results in the past year (three years is too much)◦ Developed at CCRMA◦ JOS involved as collaborator or adviser
(i.e., I know something about it!)
![Page 15: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/15.jpg)
DAFx-Related Research involving JOS at CCRMA, 2008-2009
Overview
• Previously at DAFx06
• Research Update
• CCRMA
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 5 / 54
CCRMA building: The Knoll, Stanford University
![Page 16: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/16.jpg)
Multimodal Spring ReverbModeling
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 6 / 54
![Page 17: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/17.jpg)
Accutronics Type 8 Spring Tank
Overview
Spring Reverb Models
• Spring Tank
• Impulse Response
• Model
• Sound Examples
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 7 / 54
Top: Accutronics Type 8 Spring TankBot: Single Spring “Folded” into a Compact Space
![Page 18: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/18.jpg)
Measured Single-Spring Impulse Response
Overview
Spring Reverb Models
• Spring Tank
• Impulse Response
• Model
• Sound Examples
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 8 / 54
0 50 100 150 200 250−1
−0.5
0
0.5
1spring element impulse response onset
time − milliseconds
resp
onse
am
plitu
de
spring element impulse response onset spectrogram
time − milliseconds
freq
uenc
y −
kH
z
0 50 100 150 2000
1
2
3
4
5
6level − dB
−60
−50
−40
−30
−20
−10
0
![Page 19: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/19.jpg)
Model Impulse Response
Overview
Spring Reverb Models
• Spring Tank
• Impulse Response
• Model
• Sound Examples
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 9 / 54
0 100 200 300 400 500−1
−0.5
0
0.5
1modeled spring element impulse response onset
time − milliseconds
resp
onse
am
plitu
de
modeled spring element impulse response onset spectrogram
time − milliseconds
freq
uenc
y −
kH
z
0 50 100 150 200 250 300 350 400 4500
1
2
3
4
5
6level − dB
−60
−50
−40
−30
−20
−10
0
Model Impulse Response in Time and Frequency Domains
![Page 20: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/20.jpg)
Spring Reverb Sound Examples
Overview
Spring Reverb Models
• Spring Tank
• Impulse Response
• Model
• Sound Examples
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 10 / 54
• Dry Source Signal: (WAV) (MP3)• Measured Spring-Reverb Response: (WAV) (MP3)• Spring-Reverb Model Response: (WAV) (MP3)
Submitted Paper: “A Spring Reverb Model Employing CoupledTorsional and Longitudinal Modes”
Jonathan Abel, Dave Berners, Kyle Spratt, and Julius Smith
(in review)
![Page 21: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/21.jpg)
Virtual Analog Circuits
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 11 / 54
![Page 22: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/22.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 23: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/23.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 24: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/24.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 25: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/25.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 26: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/26.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 27: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/27.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 28: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/28.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 29: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/29.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 30: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/30.jpg)
Digitizing Circuits in Real Time
Overview
Spring Reverb Models
Virtual Analog Circuits
• Real Time Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 12 / 54
Recent CCRMA/EE thesis by David Yeh :
Digital Implementation of Musical Distortion Circuits byAnalysis and Simulation — June 2009
• Analog Audio Circuits → Real-Time Digital Audio Effects• Includes work of four past DAFx papers• Linear and nonlinear methods for digitizing circuits• Nonlinear methods similar to SPICE (implicit) but modified for
real time circuit-solving (semi-implicit) in discrete time• One method extends the “K Method” to
◦ Nonlinear circuits, with automated application to “netlists”◦ Discrete-time nonlinear state-space formulation
(resolves issues with certain circuit types)
• Instantaneous nonlinearities are “precomputed” as in K Method• Can be applied to transistor and vacuum-tube circuits• Accuracy limited primarily by the underlying device models
![Page 31: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/31.jpg)
Virtual Acoustic Guitar Models
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 13 / 54
![Page 32: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/32.jpg)
Coupled Strings Analysis and Synthesis
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
• Coupled Strings
• Sound Examples
• Sound Examples
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 14 / 54
Submitted paper (from pending CCRMA/CS thesis) by Nelson Lee :
“Analysis and Synthesis of Coupled Vibrating StringsUsing a Hybrid Modal-Waveguide Synthesis Model”
Nelson Lee, Julius Smith, and Vesa Valimaki (in review)
Similar to Balazs Bank formulation, but replacing low-frequencypartials by fourth-order resonators (instead of addingsecond-order resonators to existing partials)
![Page 33: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/33.jpg)
Virtual Acoustic Guitar Sound Examples of Individual Effects
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
• Coupled Strings
• Sound Examples
• Sound Examples
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 15 / 54
From Nelson Lee’s thesis defense:
• Original waveform: (WAV) (MP3)• Simple lossless, reflectively terminated digital waveguide (DWG):
(WAV) (MP3)• Add loop filter: (WAV) (MP3)• Add interpolation filter: (WAV) (MP3)• Add excitation (ICMC07): (WAV) (MP3)• Add body response: (WAV) (MP3)• Add hybrid modal/waveguide model: (WAV) (MP3)• Exaggerate pitch glide due to tension modulation: (WAV) (MP3)
![Page 34: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/34.jpg)
Virtual Acoustic Guitar Sound Examples
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
• Coupled Strings
• Sound Examples
• Sound Examples
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 16 / 54
More Nelson Lee examples:
• Original 1: (WAV) (MP3)• Synthesized 1: (WAV) (MP3)
• Original 2: (WAV) (MP3)• Synthesized 2: (WAV) (MP3)
• Original 3: (WAV) (MP3)• Synthesized 3: (WAV) (MP3)
• Original 4: (WAV) (MP3)• Synthesized 4: (WAV) (MP3)
• Original 5: (WAV) (MP3)• Synthesized 5: (WAV) (MP3)
• Original 6: (WAV) (MP3)• Synthesized 6: (WAV) (MP3)
• Synthesized Chord Demo: (WAV) (MP3)
![Page 35: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/35.jpg)
Haptic Feedback Control forVirtual Instruments
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 17 / 54
![Page 36: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/36.jpg)
Haptic Virtual Musical Instruments
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
• Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 18 / 54
CCRMA/EE PhD student Ed Berdahl is working on
Haptic Feedback Control for Virtual Instruments
Dissertation expected by the end of the year
Goals:
• Assist and/or augment gestures• Assist with accurate playing• Recent projects:
◦ Haptically plucked virtual string◦ Active drumhead (one-handed rolls, etc.):
http://ccrma.stanford.edu/~eberdahl/Projects/-HapticDrum/
![Page 37: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/37.jpg)
Haptic Virtual Musical Instruments
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
• Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 18 / 54
CCRMA/EE PhD student Ed Berdahl is working on
Haptic Feedback Control for Virtual Instruments
Dissertation expected by the end of the year
Goals:
• Assist and/or augment gestures• Assist with accurate playing• Recent projects:
◦ Haptically plucked virtual string◦ Active drumhead (one-handed rolls, etc.):
http://ccrma.stanford.edu/~eberdahl/Projects/-HapticDrum/
![Page 38: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/38.jpg)
Haptic Virtual Musical Instruments
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
• Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 18 / 54
CCRMA/EE PhD student Ed Berdahl is working on
Haptic Feedback Control for Virtual Instruments
Dissertation expected by the end of the year
Goals:
• Assist and/or augment gestures• Assist with accurate playing• Recent projects:
◦ Haptically plucked virtual string◦ Active drumhead (one-handed rolls, etc.):
http://ccrma.stanford.edu/~eberdahl/Projects/-HapticDrum/
![Page 39: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/39.jpg)
Haptic Virtual Musical Instruments
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
• Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 18 / 54
CCRMA/EE PhD student Ed Berdahl is working on
Haptic Feedback Control for Virtual Instruments
Dissertation expected by the end of the year
Goals:
• Assist and/or augment gestures• Assist with accurate playing• Recent projects:
◦ Haptically plucked virtual string◦ Active drumhead (one-handed rolls, etc.):
http://ccrma.stanford.edu/~eberdahl/Projects/-HapticDrum/
![Page 40: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/40.jpg)
Haptic Virtual Musical Instruments
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
• Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 18 / 54
CCRMA/EE PhD student Ed Berdahl is working on
Haptic Feedback Control for Virtual Instruments
Dissertation expected by the end of the year
Goals:
• Assist and/or augment gestures• Assist with accurate playing• Recent projects:
◦ Haptically plucked virtual string◦ Active drumhead (one-handed rolls, etc.):
http://ccrma.stanford.edu/~eberdahl/Projects/-HapticDrum/
![Page 41: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/41.jpg)
Haptic Virtual Musical Instruments
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
• Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 18 / 54
CCRMA/EE PhD student Ed Berdahl is working on
Haptic Feedback Control for Virtual Instruments
Dissertation expected by the end of the year
Goals:
• Assist and/or augment gestures• Assist with accurate playing• Recent projects:
◦ Haptically plucked virtual string◦ Active drumhead (one-handed rolls, etc.):
http://ccrma.stanford.edu/~eberdahl/Projects/-HapticDrum/
![Page 42: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/42.jpg)
New Digital Oscillator Algorithms
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 19 / 54
![Page 43: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/43.jpg)
Sawtooth Waveforms via Differentiated Polynomials
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 20 / 54
Givenf(x) = xn + an−1x
n−1 + ... + a1x + a0
then differentiating n − 1 times gives
f (n)(x) = n!x + (n − 1)! an−1.
This first-order polynomial (a line segment) generates a sawtoothwaveform as x periodically traverses [−1, 1].
![Page 44: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/44.jpg)
Differentiated Polynomial Wave (DPW) Sawtooth Synthesis
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 21 / 54
1. Digitally synthesize
x(n) = f
[
2
(
nT
Pmod 1
)
− 1
]
,
wheref(x) = xn + an−1x
n−1 + ... + a1x + a0
T = sampling interval (sec)
P = desired period (sec)
n = sample number (integer)
2. Apply n − 1 first-order finite differencesxk+1(n) = [xk(n) − xk(n − 1)]/(2T/P ) to get
Xn−1(z) =
(
1 − z−1
2T/P
)n−1
X(z)
![Page 45: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/45.jpg)
Minimizing Aliasing
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 22 / 54
Initial waveform is given by sampling
f(x) = xn + an−1xn−1 + ... + a1x + a0, x ∈ [−1, 1).
After n − 1 derivatives, we get
f (n)(x) = n!x + (n − 1)! an−1.
• For zero mean, set an−1 = 0• The n − 1 remaining degrees of freedom in f(x) can be used to
maximize flatness at the transition from x = 1 to x = −1• This smoothness minimizes aliasing in the synthesized sawtooth• We can set a0 = 0 because it has no effect on smoothness• This leaves n − 2 coefficients to optimize
![Page 46: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/46.jpg)
First Several Maximum-Smoothness Examples
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 23 / 54
Results for polynomial orders up to n = 6:
f2(x) = x2
f3(x) = x3− x
f4(x) = x4− 2x2
f5(x) = x5−
10
3x3 +
7
3
f6(x) = x6− 5x4 + 7x2
Submitted Paper: “Alias-Suppressed Oscillators based onDifferentiated Polynomial Waveforms”
Vesa Valimaki, Juhan Nam, Julius Smith, and Jonathan Abel
IEEE Transactions on Acoustics, Speech, and Language ProcessingMarch 2010 (accepted for publication)
![Page 47: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/47.jpg)
Comparison of First Four Polynomial Orders
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 24 / 54
-150
-100
-50
0
50
0 0.1 0.2 0.3 0.4 0.5
Mag
nitu
de (
dB)
Normalized Frequency (cycles/sample)
Magnitude Spectra - windowed(200dB) saw case
saw1saw2saw3saw4
![Page 48: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/48.jpg)
Same Comparison over Log Frequency
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 25 / 54
-150
-100
-50
0
50
1e-05 0.0001 0.001 0.01 0.1 1
Mag
nitu
de (
dB)
Normalized Frequency (cycles/sample)
Magnitude Spectra
saw1saw2saw3saw4
![Page 49: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/49.jpg)
Relation of Aliased Components to Masking Threshold
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 26 / 54
0 5 10 15 20 25−20
0
20
40
60
80
100
Bark
SP
L [d
B]
Masking curve
Spectrum of a sawtooth waveform over masking threshold
• F0 = 4.3 kHz, Fs = 44.1 kHz• 3rd-order B-spline interpolation = 4th-order DPW
[Juhan Nam]
![Page 50: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/50.jpg)
Sound Examples
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
• Sawtooth Synth
• Diff’d Polynomials
• Aliasing Suppression
• More Examples
• Comparisons
• Comparisons LogF
• Aliasing Masked
• Sound Example
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 27 / 54
• Plain Digital Sawtooth• Differentiated-Parabolic-Wave Sawtooth• Doubly Differentiated Cubic-Wave Sawtooth
![Page 51: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/51.jpg)
Spectral Delay Filters
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 28 / 54
![Page 52: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/52.jpg)
Spectral Delay Filters
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
• Spectral Delay Filters
• Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 29 / 54
x(n) - A1(z) - A2(z) - . . . -AM (z) -Heq(z) - y(n)
Time (ms)0 1 2 3 4 5 6 7
Fre
quen
cy(k
Hz)
0
10
20
See presentation later this morning (11:20 am):
“Spectral Delay Filters with Feedback Delay and Time-VaryingCoefficients”
Jussi Pekonen, Vesa Valimaki, Jonathan Abel, and Julius Smith
![Page 53: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/53.jpg)
Spectral Delay Filters
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
• Spectral Delay Filters
• Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 30 / 54
Recent Paper (published online):
“Spectral Delay Filters”
Vesa Valimaki, Jonathan Abel, and Julius Smith
Journal of the Audio Engineering Society
July/August 2009
![Page 54: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/54.jpg)
Audio FFT Filter Banks
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 31 / 54
![Page 55: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/55.jpg)
Octave Filter Bank Schematic
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 32 / 54
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8
Filt
er G
ain
Spectral Sample Number
Complex Octave Filter Bank
Band 1Band 2Band 3Band 4
Simple octave filter bank for complex signals.
![Page 56: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/56.jpg)
Basic Idea
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 33 / 54
x3(1)
x(1)
x(2)
x(3)
x(4)
x(5)
x(6)
x(7)
x(8)
fft(8)
ifft(2)
ifft(4)
X(8)
X(1)
x1(1)
x1(2)
x1(3)
x1(4)
x2(1)
x2(2)
x4(1)
• FFT implementation of one frame of simple octave filter bank• Successive frames non-overlapping (rectangular window)
![Page 57: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/57.jpg)
Interpolated Frequency Response
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 34 / 54
-100
-80
-60
-40
-20
0
0 200 400 600 800 1000
Gai
n (d
B)
Spectral Sample Number
Interpolated128 Channel-Signal Magnitude-Spectra Overlaid
Band 1Band 2Band 3Band 4
Channel-frequency-response overlay for three-octave filter bank
• Filter-bank driven by an impulse• Zero-padded FFT taken for each channel signal• Magnitude responses overlaid
![Page 58: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/58.jpg)
Practical Octave Filter Bank
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 35 / 54
-100
-80
-60
-40
-20
0
0 500 1000 1500 2000 2500 3000 3500 4000
Gai
n (d
B)
Spectral Sample Number
Interpolated Channel Signal Spectra
Improve channel-filter impulse responses:
Rectangularly windowed sinusoids→ Chebyshev-windowed sinusoids
![Page 59: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/59.jpg)
Superposition of Channel Spectra after Critical Sampling
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 36 / 54
-100
-80
-60
-40
-20
0
0 500 1000 1500 2000 2500 3000 3500 4000
Gai
n (d
B)
Spectral Sample Number
Interpolated Channel Signal Spectra after Aliased Reconstruction
• Each channel maximually downsampled• Transition bands alias heavily• Aliasing cancels in filter-bank sum
![Page 60: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/60.jpg)
IFFT Band Allocation Including Transition Bands
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 37 / 54
-100
-80
-60
-40
-20
0
0 200 400 600 800 1000
Gai
n (d
B)
Spectral Sample Number
Channel Signal Spectra Interpolated by 4
As before but allocating wider overlapping IFFT bands:
• Passband plus transitions fit inside IFFT• Passbands contiguous as before, but IFFTs overlap more
![Page 61: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/61.jpg)
Aliasing Suppression
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 38 / 54
-100
-80
-60
-40
-20
0
0 200 400 600 800 1000
Gai
n (d
B)
Spectral Sample Number
Channel Signal Spectra Interpolated by 4 from Aliased Bands
Reconstruction after critical downsamplingAliasing is reduced because now there is no aliasing of transitionbands
![Page 62: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/62.jpg)
Real Octave Filter Bank
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 39 / 54
-100
-80
-60
-40
-20
0
0 200 400 600 800 1000
Gai
n (d
B)
Spectral Sample Number
Channel Signal Spectra Interpolated by 4
Approximate octave filter bank for real signals
![Page 63: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/63.jpg)
Notes on Audio FFT Filter Banks
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 40 / 54
• Arbitrary nonuniform spectral partitions and/or overlap-adddecompositions are easily implemented, while preserving theFFT speed advantage
• Extension to time-varying nonuniform filter banks isstraightforward
• Come see the poster this afternoon!
![Page 64: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/64.jpg)
Spectrally Matched Click Synthesis
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
• Octave Filter Bank
• Basic Idea
• Frequency Response
• Practical Response
• Critical Sampling
• Widened IFFT Bands
• Suppressed Aliasing
• Real Signals
• Notes
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 41 / 54
While outside the 1-year limit, Matt Wright’s poster this afternoon(4:30 pm) Spectrally Matched Click Synthesis is another workperformed at least partially at CCRMA with JOS input.
• FIR filter design to achieve a minimum-duration “click” having adesired magnitude spectrum
• Applications:
◦ Incremental attack strength modification◦ Continuous gradual “morphing” between an input sound and
successively more impulsive/ percussive sounds
![Page 65: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/65.jpg)
Acoustically Transparent andConfigurable Microphone Array
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 42 / 54
![Page 66: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/66.jpg)
Microphone Array
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
• Mic Array
• Mic Array Paper
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 43 / 54
• Adustable geometry (software calibrated)• Sixteen microphones (Countryman B6 Omni Lavalier):
◦ 2 mm diameter capsules◦ 1 mm diameter flexible mounting wire◦ Acoustically transparent over most of the audio band
![Page 67: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/67.jpg)
Upcoming Paper
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
• Mic Array
• Mic Array Paper
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 44 / 54
“A Configurable Microphone Array with Acoustically TransparentOmnidirectional Elements”
Jonathan Abel, Nicholas Bryan, Travis Skare, Patty Huang, DariusMostowfi, Miriam Kolar, and Julius Smith
AES-2009, New York
Current Application:
Recording and modeling acoustic properties of undergroundgalleries at pre-Inca archeological site Chavın de Huantar in Peru
![Page 68: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/68.jpg)
Flash Audio Plugins and Faust toActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 45 / 54
![Page 69: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/69.jpg)
Faust to ActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
• Faust to Flash
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 46 / 54
CCRMA/EE graduate student Travis Skare developed a Faustarchitecture file for Flash browser plugins:http://ccrma.stanford.edu/~travissk/faustflash/
• Faust generates C++ as usual• Alchemy (by Adobe Labs) translates C++ to ActionScript• Several Faust examples successfully compiled:
pitch-shifter, freeverb, karplus, osc,multibandfilter
• Interesting points to note:
◦ Flash version 10 needed for run-time sound processing◦ Delay from plugin controls to sound is about half a second
• Thanks to Google for allowing Travis to release his code as freesoftware
![Page 70: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/70.jpg)
Faust to ActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
• Faust to Flash
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 46 / 54
CCRMA/EE graduate student Travis Skare developed a Faustarchitecture file for Flash browser plugins:http://ccrma.stanford.edu/~travissk/faustflash/
• Faust generates C++ as usual• Alchemy (by Adobe Labs) translates C++ to ActionScript• Several Faust examples successfully compiled:
pitch-shifter, freeverb, karplus, osc,multibandfilter
• Interesting points to note:
◦ Flash version 10 needed for run-time sound processing◦ Delay from plugin controls to sound is about half a second
• Thanks to Google for allowing Travis to release his code as freesoftware
![Page 71: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/71.jpg)
Faust to ActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
• Faust to Flash
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 46 / 54
CCRMA/EE graduate student Travis Skare developed a Faustarchitecture file for Flash browser plugins:http://ccrma.stanford.edu/~travissk/faustflash/
• Faust generates C++ as usual• Alchemy (by Adobe Labs) translates C++ to ActionScript• Several Faust examples successfully compiled:
pitch-shifter, freeverb, karplus, osc,multibandfilter
• Interesting points to note:
◦ Flash version 10 needed for run-time sound processing◦ Delay from plugin controls to sound is about half a second
• Thanks to Google for allowing Travis to release his code as freesoftware
![Page 72: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/72.jpg)
Faust to ActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
• Faust to Flash
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 46 / 54
CCRMA/EE graduate student Travis Skare developed a Faustarchitecture file for Flash browser plugins:http://ccrma.stanford.edu/~travissk/faustflash/
• Faust generates C++ as usual• Alchemy (by Adobe Labs) translates C++ to ActionScript• Several Faust examples successfully compiled:
pitch-shifter, freeverb, karplus, osc,multibandfilter
• Interesting points to note:
◦ Flash version 10 needed for run-time sound processing◦ Delay from plugin controls to sound is about half a second
• Thanks to Google for allowing Travis to release his code as freesoftware
![Page 73: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/73.jpg)
Faust to ActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
• Faust to Flash
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 46 / 54
CCRMA/EE graduate student Travis Skare developed a Faustarchitecture file for Flash browser plugins:http://ccrma.stanford.edu/~travissk/faustflash/
• Faust generates C++ as usual• Alchemy (by Adobe Labs) translates C++ to ActionScript• Several Faust examples successfully compiled:
pitch-shifter, freeverb, karplus, osc,multibandfilter
• Interesting points to note:
◦ Flash version 10 needed for run-time sound processing◦ Delay from plugin controls to sound is about half a second
• Thanks to Google for allowing Travis to release his code as freesoftware
![Page 74: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/74.jpg)
Faust to ActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
• Faust to Flash
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 46 / 54
CCRMA/EE graduate student Travis Skare developed a Faustarchitecture file for Flash browser plugins:http://ccrma.stanford.edu/~travissk/faustflash/
• Faust generates C++ as usual• Alchemy (by Adobe Labs) translates C++ to ActionScript• Several Faust examples successfully compiled:
pitch-shifter, freeverb, karplus, osc,multibandfilter
• Interesting points to note:
◦ Flash version 10 needed for run-time sound processing◦ Delay from plugin controls to sound is about half a second
• Thanks to Google for allowing Travis to release his code as freesoftware
![Page 75: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/75.jpg)
Faust to ActionScript Conversion
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
• Faust to Flash
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 46 / 54
CCRMA/EE graduate student Travis Skare developed a Faustarchitecture file for Flash browser plugins:http://ccrma.stanford.edu/~travissk/faustflash/
• Faust generates C++ as usual• Alchemy (by Adobe Labs) translates C++ to ActionScript• Several Faust examples successfully compiled:
pitch-shifter, freeverb, karplus, osc,multibandfilter
• Interesting points to note:
◦ Flash version 10 needed for run-time sound processing◦ Delay from plugin controls to sound is about half a second
• Thanks to Google for allowing Travis to release his code as freesoftware
![Page 76: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/76.jpg)
Summary
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 47 / 54
![Page 77: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/77.jpg)
Summary
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
• Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 48 / 54
In summary, we took a quick look at some DAFx-Related Researchinvolving JOS at CCRMA in 2008-2009:
• Spring Reverb Modeling — Jonathan Abel et al. — newpropagation modes and calibration methods
• Digitizing Analog Circuits in Real Time — David Yeh —Automated K-Method for nonlinear analog circuits
• Coupled Strings Analysis and Synthesis — Nelson Lee —Fourth-order modes for low partials, wavuide model for upperpartials; new analysis techniques
• Haptic Virtual Instruments — Ed Berdahl — Real controllers (withforce feedback) for virtual instruments
![Page 78: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/78.jpg)
Summary, continued
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
• Summary
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 49 / 54
• Alias-Suppressed Virtual Analog — Vesa Valimaki et al. —differentiated higher-order polynomials suppress aliasing furtherthan in the parabolic case (Valimaki 2005)
• Spectral Delay Filters — Vesa Valimaki et al. — “impulseresponse synthesis”
• Audio FFT Filter Banks — JOS — arbitrary nonuniform filterbanks (spectral overlap-add decompositions) using overlappingIFFTs for each subband that include transition bands
• Microphone Array — Jonathan Abel et al. — Acousticallytransparent, configurable, software-calibrated microphone arrayfor sampling the 3D sound field
• Faust to Flash Plugins — Travis Skare — Tools for making Flashplugins from Faust source
![Page 79: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/79.jpg)
Further Details on DifferentiatedPolynomial Synthesis
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
SummaryFurther Details onDifferentiatedPolynomial Synthesis
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 50 / 54
![Page 80: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/80.jpg)
Maximum Smoothness Problem Formulation
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Further Details onDifferentiatedPolynomial Synthesis
• Max Smoothness
• Even-Odd Parts
• Even-Odd Properties
• Simplified Solution
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 51 / 54
For maximum wraparound smoothness, compute an,n ∈ [1, n − 2], such that
f (k)(−1) = f (k)(1)
for k = 0, 1, . . . , n − 1.
• These equations yield an upper triangular system• Triangular matrix equations are easily “back-solved”• Solution gives the maximually flat coefficients for f(x)
![Page 81: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/81.jpg)
Even and Odd Polynomials
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Further Details onDifferentiatedPolynomial Synthesis
• Max Smoothness
• Even-Odd Parts
• Even-Odd Properties
• Simplified Solution
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 52 / 54
In general, f(x) is a sum of its even and odd parts:
f(x) = fe(x) + fo(x)
wherefe(−x) = fe(x)
∆=
f(x) + f(−x)
2
−fo(−x) = fo(x)∆=
f(x) − f(−x)
2
• Even part fe(x) contains all even powers of x:
fe(x) = · · · + a4x4 + a2x
2 + a0
• Odd part fo(x) contains all odd powers of x:
fo(x) = · · · + a5x5 + a3x
3 + a1x
![Page 82: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/82.jpg)
Solution Properties of Even and Odd Polynomials
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Further Details onDifferentiatedPolynomial Synthesis
• Max Smoothness
• Even-Odd Parts
• Even-Odd Properties
• Simplified Solution
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 53 / 54
We havef(x) = fe(x) + fo(x)
where
fe(x) =f(x) + f(−x)
2
fo(x) =f(x) − f(−x)
2
• Note that fe(−1) = fe(1) ⇒ smoothness constraint satisfiedspontaneously by even part
• Since fo(−1) = −fo(1), we must have fo(1) = 0⇒ sum of fo coefficients must be zero in odd part
![Page 83: Recent CCRMA Research in Digital Audio Synthesis ...dafx09.como.polimi.it/data/DAFx09KeynoteIII.pdf · Recent CCRMA Research in Digital Audio Synthesis, Processing, and Effects Julius](https://reader037.fdocuments.net/reader037/viewer/2022090607/605d59f24c16c04c2814362c/html5/thumbnails/83.jpg)
Simplified Maximum Smoothness Solution
Overview
Spring Reverb Models
Virtual Analog Circuits
Acoustic Guitar Models
Haptic Instruments
New Oscillators
Spectral Delay Filters
Audio FFT Filter Banks
Microphone Array
Faust to Flash Plugins
Summary
Further Details onDifferentiatedPolynomial Synthesis
• Max Smoothness
• Even-Odd Parts
• Even-Odd Properties
• Simplified Solution
Julius O. Smith III DAFx-09, Keynote III, Como, Italy – 54 / 54
• If f(x) is an odd-order polynomial satisfyingf (k)(−1) = f (k)(1) for k = 0, 1, . . . , n − 1, then it continuesto satisfy those constraints when its even part is replaced by zero
• Similarly, the odd part of an even-order polynomial f(x) may beset to zero without affecting its wraparound smoothness
• Thus, without loss of generality, the starting polynomial f(x) maybe taken as even or odd, according its order
• The derivative of an even polynomial is odd, and vice versa
• Every other polynomial derivative has the sum-to-zero constraint
• Upper triangular system is reduced by about half