LING 520 Introduction to Phonetics I · 2008. 9. 29. · LING 520 Introduction to Phonetics I, Fall...
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LING 520 Introduction to Phonetics I LING 520 Introduction to Phonetics I Fall 2008 Fall 2008 Week Week 4 4 Basic acoustics Fourier transform and LTI systems Recording and sampling Oct. 1, 2008
Transcript of LING 520 Introduction to Phonetics I · 2008. 9. 29. · LING 520 Introduction to Phonetics I, Fall...
LING 520 Introduction to Phonetics ILING 520 Introduction to Phonetics I
Fall 2008Fall 2008
WeekWeek 44
Basic acoustics
Fourier transform and LTI systems
Recording and sampling
Oct. 1, 2008
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=+ kxdt
xdm
mkùtAx =+= 00 ,)cos(
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• displacement: momentary distance from restpoint B
• cycle: one complete oscillation
• amplitude: maximum displacement
• frequency: number of cycles per second (hertz or Hz)
• period: number of seconds per cycle
• phase: portion of a cycle through which a waveform hasadvanced relative to some arbitrary reference point
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wave 1: 440Hz
wave 2: 330Hz
wave 1 + 2: ? Hz
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00 N/m102 ,)log(10)log(20 === pppppSPL
212
00 rwatts/mete10 ),/(log10 == IIIIL
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• Fourier's theorem:
Any periodic signal (must satisfy Dirichlet conditions) iscomposed of a superposition of pure sine waves, whosefrequencies are harmonics of the fundamental frequency of thesignal.
• The fundamental frequency F0 determines the perceived pitchof the sound (In reality, perceived pitch is determined by thespacing harmonics as much as by F0)
• The harmonic frequencies change the quality or timbre of thesound.
...3sin2sinsin
...3cos2coscos
)sincos()(
321
3210
1
0
++++
++++=
++==
xbxbxb
xaxaxaa
nxbnxaaxfn
nn
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• A waveform can be represented as a spectrum showing:
• Transmission of Component frequencies on the x-axis• Intensity (Amplitude) of each component on on the y-axis
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• A spectrogram displays:
• Time along the x-axis• Component frequencies along the y-axis• Intensity (Amplitude) using darkness
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H (T{.})x [n] y [n]
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]}[{]}[{]}[][{ 2121 nxbTnxaTnbxnaxT +=+
][][ 21 nbxnax + ][][ 21 nbynay +
][ 01 nny
][2 nx][1 ny ][2 ny
][ 01 nnx
][1 nx
][1 nx ][1 ny
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==
otherwise 0
0 if 1][
nn
)][][(][=
=k
knkxnx
][n ][nh
==k
knkxTny ][][][ { }=
=k
knTkxny ][][][
][*][][ nnxnx =
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• The Fourier transform of a convolution is the product ofthe Fourier transforms
• The Fourier transform of a product is the convolution ofthe Fourier transforms
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Recording
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Recording
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Recording
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Recording
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• Classroom recording (SNR 29 dB)
• Laptop recording (SNR 44 dB)
• Professional recording (SNR 90 dB)
[From: Chilin Shih]
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Recording
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[From: Chilin Shih]
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Sampling
• In order to transform sound into a digital format, you must sample the
sound. The computer takes a snapshot of the sound level at small time
intervals while you are recording.
• The number of samples taken each second is called the sampling
rate. The more samples that are taken, the better sound quality. But we
also need more storage space for higher quality sound.
44100 Hz
22050 Hz
11025 Hz
8000 Hz
5000 Hz
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Quantization
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Sound file formats
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Sound file formats
wav 550K
mp3 51K
wav->mp3->wav
[From: Chilin Shih]
