By Sarita Jondhale1 Signal Processing And Analysis Methods For Speech Recognition

By Sarita Jondhale 1

Signal Processing And Analysis Methods For Speech

Recognition


Introduction

• Spectral analysis is the process of defining the speech in different parameters for further processing

• Eg short term energy, zero crossing rates, level crossing rates and so on

• Methods for spectral analysis are therefore considered as core of the signal processing front end in a speech recognition system


Spectral Analysis models

• Pattern recognition model• Acoustic phonetic model


Spectral Analysis Model

Parameter measurement is common in both the systems


Pattern recognition Model

• The three basic steps in pattern recognition model are – 1. parameter measurement– 2. pattern comparison– 3. decision making


1. Parameter measurement

• To represent the relevant acoustic events in speech signal in terms of compact efficient set of speech parameters

• The choice of which parameters to use is dictated by other consideration

• eg – computational efficiency, – type of Implementation ,– available memory

• The way in which representation is computed is based on signal processing considerations


Acoustic phonetic Model


Spectral Analysis

• Two methods:

– The Filter Bank spectrum

– The Linear Predictive coding (LPC)


The Filter Bank spectrum

Digital i/p

Spectral representation

The band pass filters coverage spans the frequency range of interest in the signal


1.The Bank of Filters Front end Processor

• One of the most common approaches for processing the speech signal is the bank-of-filters model

• This method takes a speech signal as input and passes it through a set of filters in order to obtain the spectral representation of each frequency band of interest.


• Eg• 100-3000 Hz for telephone quality

signal• 100-8000 Hz for broadband signal• The individual filters generally do

overlap in frequency• The output of the ith bandpass filter• where Wi is the normalized frequency


• Each bandpass filter processes the speech signal independently to produce the spectral representation Xn


The Bank of Filters Front end Processor



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The sampled speech signal, s(n), is passed through a bank of Q Band pass filters, giving the signals



The bank-of-filters approach obtains the energy value of the speech signal considering the following steps:

• Signal enhancement and noise elimination.- To make the speech signal more evident to the bank of filters.

• Set of bandpass filters.- Separate the signal in frequency bands. (uniform/non uniform filters )


• Nonlinearity.- The filtered signal at every band is passed through a non linear function (for example a wave rectifier full wave or half wave) for shifting the bandpass spectrum to the low-frequency band.



• Low pass filter.- This filter eliminates the high-frequency generated by the non linear function.

• Sampling rate reduction and amplitude compression.- The resulting signals are now represented in a more economic way by re-sampling with a reduced rate and compressing the signal dynamic range.

The role of the final lowpass filter is to eliminate the undesired spectral peaks



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Types of Filter Bank Used For Speech Recognition

• uniform filter bank• Non uniform filter bank


uniform filter bank

• The most common filter bank is the uniform filter bank

• The center frequency, fi, of the ith bandpass filter is defined as

• Q is number of filters used in bank of filters

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torequired filters spaceduniformly ofnumber theis N

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uniform filter bank

• The actual number of filters used in the filter bank

• bi is the bandwidth of the ith filter

• There should not be any frequency overlap between adjacent filter channels

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uniform filter bank

If bi < Fs/N, then the certain portions of the speech spectrum would be missing from the analysis and the resulting speech spectrum would not be considered very meaningful


nonuniform filter bank

• Alternative to uniform filter bank is nonuniform filter bank

• The criterion is to space the filters uniformly along a logarithmic frequency scale.

• For a set of Q bandpass filters with center frequncies fi and bandwidths bi, 1≤i≤Q, we set


nonuniform filter bank

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• The most commonly used values of α=2

• This gives an octave band spacing adjacent filters

• And α=4/3 gives 1/3 octave filter spacing


Implementations of Filter Banks

• Depending on the method of designing the filter bank can be implemented in various ways.

• Design methods for digital filters fall into two classes:– Infinite impulse response (IIR)

(recursive filters)– Finite impulse response


The FIR filter: (finite impulse response) or non recursive filter

• The present output is depend on the present input sample and previous input samples

• The impulse response is restricted to finite number of samples


• Advantages: – Stable, noise less sever– Excellent design methods are available

for various kinds of FIR filters– Phase response is linear

• Disadvantage:– Costly to implement– Memory requirement and execution

time are high– Require powerful computational facilities


The IIR filter: (Infinite impulse response) or recursive filter

• The present output sample is depends on the present input, past input samples and output samples

• The impulse response extends over an infinite duration


• Advantage:– Simple to design– Efficient

• Disadvantage:– Phase response is non linear– Noise affects more– Not stable


FIR Filters

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FIR Filters• Less expensive implementation can be

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Frequency Domain Interpretation For Short Term

Fourier Transformmjw

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At n=n0

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Where FT[.] denotes Fourier TransformSn0(eji) is the conventional Fourier transform of the windowed signal, s(m)w(n0-m), evaluated at the frequency = i

A



Fourier Transform

Shows which part of s(m) are used in the computation of the short time Fourier transform



Fourier Transform• Since w(m) is an FIR filter with size L

then from the definition of Sn(eji) we can state that– If L is large, relative to the signal

periodicity then Sn(eji) gives good frequency resolution

– If L is small, relative to the signal periodicity then Sn(eji) gives poor frequency resolution



Fourier TransformFor L=500 points Hamming window is applied to a section of voiced speech.

The periodicity of the signalis seen in the windowed timewaveform as well as in the short time spectrum in whichthe fundamental frequencyand its harmonics show up asnarrow peaks at equally spaced frequencies.



Fourier TransformFor short windows, the time sequence s(m)w(n-m) doesn’t show the signal periodicity, nor does the signal spectrum.It shows the broad spectral envelop very well.



Fourier Transform

Shows irregular series of local peaks and valleys due to the random nature of the unvoiced speech



Fourier Transform

Using the shorter window smoothes out the random fluctuations in the short time spectral magnitude and shows the broad spectral envelope very well


Linear Filtering Interpretation of the short-time Fourier

Transform• The linear filtering interpretation of

the short time Fourier Transform

• i.e Sn(ejwi) is a convolution of the low pass window, w(n), with the speech signal, s(n), modulated to the center frequency wi

)()( )( nenseSn njwjw ii * From A


FFT Implementation of Uniform Filter Bank Based on the Short-

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FFT Implementation of Uniform Filter Bank Based on the Short-

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FFT Implementation of Uniform Filter Bank Based on The Short Time FT

The FFT implementation is more efficient than the direct form structure


Nonuniform FIR Filter Bank Implementations

The most general form of a nonuniform FIR filter bank



• The kth bandpass filter impulse response, hk(n), represents a filter with a center frequency k, and bandwidth k.

• The set of Q bandpass filters covers the frequency range of interest for the intended speech recognition application



• Each band pass filter is implemented via a direct convolution

• Each band pass filter is designed via the windowing design method

• The composite frequency response of the Q-channel filter bank is independent of the number and distribution of the individual filters



A filter bank with the three filters has the exact same composite frequency responseas the filter bank with the seven filters shown in figure above



• The impulse response of the kth bandpass filter

• The frequency response of the kth bandpass filter

)()()( nhnwnh kk

FIR windowImpulse response of idealband pass filer

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• Where wmin is the lowest frequency in the filter bank and wmax is the highest frequency

• Equation 1 can be written as

• Which is independent of the number of ideal filters, Q, and their distribution in the frequency

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FFT-Based Nonuniform Filter Banks

• By combining two or more uniform channels the nonuniformity can be created

• Consider taking an N-point DFT of the sequence x(n)

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FFT-Based Nonuniform Filter Banks

• The equivalent kth channel value, Xk’ can be obtained by weighing the sequence, x(n) by the complex sequence 2 exp(-j (n/N))cos(n/N).

• If more than two channels are combined, then a different equivalent weighing sequence results


Tree Structure Realizations of Nonuniform Filter Banks

In this method the speech signal is filtered in the stages, and the sampling rate is successively reduced at each stage





• The original speech signal, s(n), is filtered initially into two bands, a low band and a high band

• The high band is down sampled by 2 and represents the highest octave band (/2≤≤ ) of the filter bank.

• The low band is similarly down sampled by 2 and fed into second filtering stage in which the signal is again split into two equal bands.

• Again the high band of the stage 2 is down sampled by 2 and is used as a next highest filter bank output.



• The low band is also down sampled by 2 and fed into a third stage of filters

• These third stage output after down sampling by factor 2, are used as the two lowest filter bands


Summary of considerations for speech recognition filter banks 1st.Type of digital filter used (IIR

(recursive) or FIR (nonrecursive))• IIR: Advantage: simple to implement and

efficient. Disadvantage: phase response is

nonlinear• FIR: Advantage: phase response is linear

Disadvantage: expensive in implementation


Summary of considerations for speech recognition filter banks2nd. The number of filters to be used in

the filter bank.1. For uniform filter banks the number of filters,

Q, can not be too small or else the ability of the filter bank to resolve the speech spectrum is greatly damaged. The value of Q less than 8 are generally avoided

2. The value of Q can not be too large, because the filter bandwidths would eventually be too narrow for some talker (eg. High-pitch females) i.e no prominent harmonics would fall within the band. (in practical systems the value of Q≤32).


Summary of considerations for speech recognition filter banks

In order to reduce overall computation, many practical systems have used nonuniform spaced filter banks


Summary of considerations for speech recognition filter banks3rd. The choice of nonlinearity and

LPF used at the output of each channel

• Nonlinearity: Full wave or Half wave rectifier

• LPF: varies from simple integrator to a good quality IIR lowpass filter.


Documents

By Sarita Jondhale1 Signal Processing And Analysis Methods For Speech Recognition