Speech Signal Representations I

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Speech Signal Representations I

• Seminar Speech Recognition 2002
• F.R. Verhage

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Speech Signal Representations I

• Decomposition of the speech signal (xn) as a
  source (en) passed through a linear
  time-varying filter (hn).

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Speech Signal Representations I

• Estimation of the filter, inspired by
• Speech production models
• Linear Predictive Coding (LPC)
• Cepstral analysis
• Speech perception models (part II)
• Mel-frequency cepstrum
• Perceptual Linaer Prediction (PLP)
• Speech recognizers estimate filter
  characteristics and ignore the source

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Speech Signal Representations IShort-Time
Fourier Analysis

• Spectrogram
• Representation of a signal highlighting several
  of its properties based on short-time Fourier
  analysis
• Two dimensional time horizontal and frequency
  vertical
• Third dimension gray or color level indicating
  energy

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Speech Signal Representations IShort-Time
Fourier Analysis

• Spectrogram
• Narrow band
• Long windows (gt 20 ms) ?
• Narrow bandwidth
• Lower time resolution, better frequency
  resolution
• Wide band
• Short windows ( lt10 ms) ?
• Wide bandwidth
• Good time resolution, lower frequency resolution
• Pitch synchronous
• Requires knowledge of local pitch period

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Speech Signal Representations IShort-Time
Fourier Analysis

• Spectrogram

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Speech Signal Representations IShort-Time
Fourier Analysis

• Window analysis
• Series of short segments, analysis frames
• Short enough so that the signal is stationary
• Usually constant, 20-30 ms
• Overlaps possible
• Different types of window functions (wmn)
• Rectangular (equal to no window function)
• Hamming
• Hanning

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Speech Signal Representations IShort-Time
Fourier Analysis

• Window analysis
• Window size must be long enough
• Rectangular N M
• Hamming, Hanning N 2M
• Pitch period not known in advance ?
• Prepare for lowest pitch period ?
• At least 20ms for rectangular or 40ms for
  Hamming/Hanning (50Hz)
• But longer windows give a more average spectrum
  instead of distinct spectra ?
• Rectangular window has better time resolution

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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis

• Window analysis
• Frequency response not completely zero outside
  main lobe ? Spectral leakage
• Second lobe of a Hamming window is approx. 43dB
  below main lobe ? less spectral leakage
• Hamming, Hanning, triangular windows offer less
  spectral leakage ?
• Rectangular windows are rarely used despite their
  better time resolution

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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis
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Speech Signal Representations IShort-Time
Fourier Analysis

• Short-time spectrum of male voice speech
• Time signal /ah/local pitch 110Hz
• 30ms rectangularwindow
• 15ms rectangular window
• 30ms Hammingwindow
• 15ms Hammingwindow

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Speech Signal Representations IShort-Time
Fourier Analysis

• Short-time spectrum of female voice speech
• Time signal /aa/local pitch 200Hz
• 30ms rectangularwindow
• 15ms rectangular window
• 30ms Hammingwindow
• 15ms Hammingwindow

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Speech Signal Representations IShort-Time
Fourier Analysis

• Short-time spectrum of unvoiced speech
• Time signal
• 30ms rectangularwindow
• 15ms rectangular window
• 30ms Hammingwindow
• 15ms Hammingwindow

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Speech Signal Representations ILinear
Predictive Coding

• LPC a.k.a. auto-regressive (AR) modeling
• All-pole filter is good approximation of speech,
  with p as the order of the LPC analysis
• Predicts current sample as linear combination of
  past p samples

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Speech Signal Representations ILinear
Predictive Coding

• To estimate predictor coefficients (ak), use
  short-term analysis technique
• Per segment, minimize the total prediction error
  by calculating the minimum squared error
• Take the derivative, equate it to 0 expressed as
  a set of p linear equationsthe Yule-Walker
  equations

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Speech Signal Representations ILinear
Predictive Coding

• Solution of the Yule-Walker equations
• Any standard matrix inversion package
• Due to the special form of the matrix, efficient
  solutions
• Covariance methodusing the Cholesky
  decomposition
• Autocorrelation methodusing windows, results in
  equations with Toeplitz matrices, solved by the
  Durbin recursion algorithm
• Lattice methodequivalent to Levinson Durbin
  recursionoften used in fixed-point
  implementations because lack of precision doesnt
  result in unstable filters

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Speech Signal Representations I Linear
Predictive Coding
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Speech Signal Representations I Linear
Predictive Coding
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Speech Signal Representations ILinear
Predictive Coding

• Spectral analysis via LPC
• All-pole (IIR) filter
• Peaks at the roots of the denominator

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Speech Signal Representations ILinear
Predictive Coding

• Prediction error
• Should be (approximately) the excitation
• Unvoiced speech, expect white noise OK
• Voiced speech, expect impulse train NOK
• All-pole assumption not altogether valid
• Real speech not perfectly periodic
• Pitch synchronous analysis gives better results
• LPC order
• Larger p gives lower prediction errors
• Too large a p results in fitting the individual
  harmonics ?separation between filter and source
  will not be so good

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Speech Signal Representations ILinear
Predictive Coding

• Prediction error
• Inverse LPC filter gives residual signal

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Speech Signal Representations ILinear
Predictive Coding

• Alternatives for the predictor coefficients
• Line Spectral Frequencies
• local sensitivity
• efficiency
• Reflection Coefficients
• Guaranteed stable ? useful for coefficient
  interpolated over time
• Log-area ratios
• Flat spectral sensitivity
• Roots of the polynomial
• Represent resonance frequencies and bandwidths

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Speech Signal Representations ICepstral
Processing

• A homomorphic transformation converts a
  convolution into a sum

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Speech Signal Representations ICepstral
Processing
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Speech Signal Representations ICepstral
Processing