Speech Signal Processing 1

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Introduction To Speech Processing

CSLU, OGI , OHSU

June 2010


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Outline

What is the Speech Processing Applications of Speech Processing

Review of Signal Processing

Fourier series Convolution Fourier Transform


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What is the Speech Processing

Speech processing is the application of digitalsignal processing ( DSP) technique to the

processing and analysis of speech signals


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Applications of Speech Processing

Speech Coding Speech recognition Speaker Verification\Identification Speech Enhancement Speech Synthesis ( Text to Speech) Disease Diagnosis


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Speech Signal

/Southampton /s/ /ou/ /th/ /aa/ /m/ /p/ /t/ /a/ /n/


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Speech Signal

/seven o eight/


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Review of Signal Processing

Analog SignalSignals that are continuous in Time. Most environmental

signals are continuous-time signals.

Digital SignalThese are created by quantizing and sampling continuous-

time signals or as data signals (e.g., stock market price

fluctuations).


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Processing Real Signals

Most of the signals in our environment are analog such assound, temperature and light

To processes these signals with a computer, we must:

1. convert the analog signals into electrical signals, e.g., using atransducer such as a microphone to convert sound into electricalsignal

2. digitize these signals, or convert them from analog to digital,using an ADC (Analog to Digital Converter)


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Analog Signal

Digital Signalspeech: 8 kbps (8bit * 1k sample)/s

256 kbps


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Discrete-Time Signals A sequence of numbers Mathematical representation:

x = {x[n]}, < n <

Sampled from an analog signal, xa (t), at time t = nT,x[n] = xa (nT ), < n <

T is called the sampling period, and its reciprocal, F =1/T, is called the sampling frequency

SF=8000Hz T =1/8000=125sec

SF=10000Hz T =1/10000=100sec

SF=16000Hz T =1/16000=62.5sec

SF=40000Hz T=1/40000=25sec


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Processed signal may need to be converted back to ananalog signal before being passed to an actuator (e.g., a

loudspeaker)

Digitaltoanalog conversion can be done by a DAC(DigitaltoAnalog Converter).

Speech Enhancement, Speech Synthesis


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Signal Processing

Time-Domain Signal ProcessingAnalyzing of the signal with respect to time. A time-domain graph

shows how a signal changes over time.

Frequency-Domain Signal ProcessingSignals are converted from time domain to the frequency domain

usually through the Fourier transform. The most common purposefor analysis of signals in the frequency domain is analysis of signal

properties.


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Fourier series A Fourier series is an expansion of a periodic function in

terms of an infinite sum of sines and cosines.

The computation and study of Fourier series is known asharmonic analysis and is extremely useful as a way tobreak up an arbitrary periodic function into a set ofsimple terms.

The periodic function can be represented in compactform.


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Fourier series


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Fourier series

N = 1

N = 3

N = 5

N = 7


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Fourier series


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Convolution

A convolution is an integral that expresses the amount ofoverlap of one function x as it is shifted over another

functionh

.

Visual explanation of convolution: http://en.wikipedia.org/wiki/Convolution


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Discrete-Time Convolution

1. Flip (reverse) one of the digital functions.2. Shift it along the time axis by one sample.3. Multiply the corresponding values of the two digital functions.4.

Summate the products from step 3 to get one point of the digitalconvolution.

5. Repeat steps 1-4 to obtain the digital convolution at all times that thefunctions overlap.

Basic steps


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LTI (Linear Time-Invariant) Systems

Convolution can describe the effect of an LTI system on asignal

Assume we have an LTI system H, and its impulseresponse h[n]

Then if the input signal is x[n], the output signal is y[n] =x[n] * h[n]

Hx[n] y[n] = x[n]*h[n]


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Fourier Transform

Definition

The Fourier transform can be thought of as a function that measureshow much of each individual frequency is present in our function

A function can be described by a summation of waves with differentamplitudes and phases.


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Fourier Transform


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Discrete Fourier Transform

Definition

In practice, we often deal with discrete functions (digital signals, forexample)

Discrete version of the Fourier Transform is much more useful insignal processing


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Question?

Speech Signal Processing 1

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