Chap 6' Speech signal Representations

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Chap 6. Speech signal Representations

• Short-time Fourier analysis
• (1) Speech signal is time-variant
• (2) Short-time stationary
• (3) time domain ? Frequency domain using FFT
• (4) Windowing function (FFT size)
• Hamming window was the most frequently
  used one.
• For 8KHz, window size 256 (240, 30ms)
  (zero-pending)
• For 16KHz, window size 512 (480, 30ms)
• (5) Spectrograms
• Narrow band, wide band spectrogram (FFT
  resolution, output filter)

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Source filter Model
Nostrils all-pole model is not good enough
The lips model Usually using 1-?z-1 ? 0.9,
0.95, 0.97
All-poles model (LPC)
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Linear Prediction Coding (LPC)

• Linear prediction (AR model)
• According to losses tube model (lattice formula
  which will introduce later)
• 8KHz sampling, c340 m/s, L 17cm ? N8 (2 poles
  for 1KHz)

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• Solve the linear prediction coefficients using
  MMSE criterion

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• Covariance method

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• Solution of covariance method using Cholesky
  decomposition
• (1) solve V, D

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• (2) solve A

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• Autocorrelation Method

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• R is Toepliz
• Using Levinson Dubins algorithm

The algorithm is to transfer Ladder filter ?
Lattice filter lattice filter ? cascade form Ei
the square error of prediction Ki the
coefficients of lattice filter refection
coefficients
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• Lattice filter
• Define forward/backward prediction errors

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• LPC using Lattice filter

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Spectral analysis vs. LPC

• LPC spectrum

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• Prediction error vs. LPC order

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Conversion between parameters

• Reflection coefficients vs. LPC
• Log-area ratios

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Cepstral processing

• Spectral vs. Cepstral
• Cepstral is a homomorphic transformation
  (de-convolution)
• The Block diagram

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• Cepstral of real signal

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• Cepstrum of pole-zero function

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LPC derived cepstrum

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• Cepstrum of speech signal
• periodic excitation train
• ? impulse train with same period in
  cepstrum-domain
• Cepstrum of windowing signal
• Example
• (from Fundamentals of Speech Recognition, by B.
  H. Juang)

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Mel-frequency Cepstrum (MFCC)

• Change the frequency scale into Mel-scale

Frequency quantiztion?
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• M20 for Fs8KHz, 24 for Fs16KHz

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Pitch detector of speech signal

• Speech signal is a quasi-periodic signal, because
  the speech is a time-variated signal.
• Find the pitch frequency (Fundamental freq., F0)
  
• ? find the period of a discrete signal.
• Assume the pitch contour will continue
• ? find a smooth pitch contour
• ? smoothing/contour tracking algorithm is
  needed.

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• Autocorrelation method
• - autocorrelation function of a periodic signal
  is also periodic, ? finding the time shift with
  max autocorrelation ? period

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• An example of Autocorrelation and pitch contour
• Half pitch/Double pitch error?
• U/V decision?
• Smoothness of pitch contour?

Max picking range? Global or Local max?
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• Normalized Cross-correlation method - used
  cross-correlation instead of
• Decaying the Normalized
• Cross-correlation
• wrt. to T?

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• Pitch tracking
• ? leave more candidates in each frame
• ? define a cost function
• ? Viterbi search