Signal Processing And Analysis Methods For Speech Recognition

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Signal Processing And Analysis Methods For Speech
Recognition
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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

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Spectral Analysis methods

• Two methods
• The Filter Bank spectrum
• The Linear Predictive coding (LPC)

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Spectral Analysis models

• Pattern recognition model
• Acoustic phonetic model

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Spectral Analysis Model
Parameter measurement is common in both the
systems
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Pattern recognition Model

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

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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

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Acoustic phonetic Model
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Spectral Analysis

• Two methods
• The Filter Bank spectrum
• The Linear Predictive coding (LPC)

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The Filter Bank spectrum
Spectral representation
Digital i/p
The band pass filters coverage spans the
frequency range of interest in the signal
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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.

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• 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

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

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

• 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 )

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• 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.

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The Bank of Filters Front end Processor

• 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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The Bank of Filters Front end Processor
Assume that the output of the ith bandpass filter
is a pure sinusoid at frequency ?I If full
wave rectifier is used as the nonlinearity
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The Bank of Filters Front end Processor


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Types of Filter Bank Used For Speech Recognition

• uniform filter bank
• Non uniform filter bank

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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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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 lt 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

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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, 1iQ, we set

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nonuniform filter bank
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• The most commonly used values of a2
• This gives an octave band spacing adjacent
  filters
• And a4/3 gives 1/3 octave filter spacing

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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

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• 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

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• 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

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• 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

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• Advantage
• Simple to design
• Efficient
• Disadvantage
• Phase response is non linear
• Noise affects more
• Not stable

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FIR Filters
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FIR Filters

• Less expensive implementation can be derived by
  representing each bandpass filter by a fixed low
  pass window ?(n) modulated by the complex
  exponential

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Frequency Domain Interpretation For Short Term
Fourier Transform
A
At nn0
Where FT. denotes Fourier Transform Sn0(ej?i)
is the conventional Fourier transform of the
windowed signal, s(m)w(n0-m), evaluated at the
frequency ? ?i
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Frequency Domain Interpretation For Short Term
Fourier Transform
Shows which part of s(m) are used in the
computation of the short time Fourier transform
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Frequency Domain Interpretation For Short Term
Fourier Transform

• Since w(m) is an FIR filter with size L then from
  the definition of Sn(ej?i) we can state that
• If L is large, relative to the signal periodicity
  then Sn(ej?i) gives good frequency resolution
• If L is small, relative to the signal periodicity
  then Sn(ej?i) gives poor frequency resolution

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Frequency Domain Interpretation For Short Term
Fourier Transform
For L500 points Hamming window is applied to a
section of voiced speech. The periodicity of
the signal is seen in the windowed time waveform
as well as in the short time spectrum in
which the fundamental frequency and its harmonics
show up as narrow peaks at equally spaced
frequencies.
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Frequency Domain Interpretation For Short Term
Fourier Transform
For short windows, the time sequence s(m)w(n-m)
doesnt show the signal periodicity, nor does
the signal spectrum. It shows the broad spectral
envelop very well.
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Frequency Domain Interpretation For Short Term
Fourier Transform
Shows irregular series of local peaks and
valleys due to the random nature of the unvoiced
speech
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Frequency Domain Interpretation For Short Term
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
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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

From A

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FFT Implementation of Uniform Filter Bank Based
on the Short-Time FT
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FFT Implementation of Uniform Filter Bank Based
on the Short-Time FT
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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

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Nonuniform FIR Filter Bank Implementations
The most general form of a nonuniform FIR filter
bank
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Nonuniform FIR Filter Bank Implementations

• 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

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Nonuniform FIR Filter Bank Implementations

• 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

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Nonuniform FIR Filter Bank Implementations
A filter bank with the three filters has the
exact same composite frequency response as the
filter bank with the seven filters shown in
figure above
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Nonuniform FIR Filter Bank Implementations

• The impulse response of the kth bandpass filter
• The frequency response of the kth bandpass filter

Impulse response of ideal band pass filer
FIR window

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Nonuniform FIR Filter Bank Implementations

• Thus the frequency response of the composite
  filter bank

1

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Nonuniform FIR Filter Bank Implementations

• 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

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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

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Tree Structure Realizations of Nonuniform Filter
Banks
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Tree Structure Realizations of Nonuniform Filter
Banks

• 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.

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Tree Structure Realizations of Nonuniform Filter
Banks

• 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

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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

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Summary of considerations for speech recognition
filter banks

• 2nd. The number of filters to be used in the
  filter bank.
• 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
• 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 Q32).

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Summary of considerations for speech recognition
filter banks

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

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Summary of considerations for speech recognition
filter banks

• 3rd. 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.

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