Linear Predictive Coding for Speech Compression

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Linear Predictive Coding for Speech Compression

• Dev Ghosh
• ECE 463

9 March 2006
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Overview

• General Model for Speech Synthesis
• Channel Vocoder
• Linear Predictive Coder (LPC-10)
• Code Excited Linear Prediction (CELP)
• Novel Application
• Sub-band adaptive filtering based on cochlear
  model

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Model for Speech Synthesis

• Speech produced by forcing air through vocal
  cords, larynx, pharynx, mouth and nose
• At transmitter speech is divided into segments
• Each segment analyzed to determine excitation
  signal and parameters of vocal tract filter

Excitation Source
Vocal tract filter
Speech
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Channel Vocoder - analysis

• Each segment of input speech analyzed by a bank
  of (bandpass) analysis filters
• Energy at output of each filter is estimated 50
  times a second and transmitted to receiver
• Decision made whether segment
• voiced /a/, /e/, /o/ or
• unvoiced /s/, /f/
• Estimate of pitch period (period of fundamental
  harmonic) is determined

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Voice vs. Unvoiced Speech
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Channel vocoder - synthesis

• Vocal tract filter implemented by bank of
  (bandpass) synthesis filters
• For voiced segments, periodic pulse generator is
  input
• For unvoiced segments, pseudonoise source is
  input
• Period determined by pitch estimate
• Scaled by output of energy estimate
• First approach to speech compression

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Linear Predictive Coder

• Models vocal tract as a single linear filter
• yn ?aiyn-iG?n
• Output yn, Input ?n, Gain G
• Input is random noise (unvoiced) or periodic
  pulse (voiced)
• LPC-10 is a standard (2.4 kb, 8000 Samples/sec)

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LPC - Voiced/Unvoiced Decision

• Voiced speech has more energy and lower frequency
  than unvoiced
• Speech segment lowpass filtered, energy at output
  relative to background noise used to determine
• Zero-crossings counted to determine frequency
• Continuity critereon voicing decision of
  neighboring frames taken into account

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LPC - Estimating Pitch Period

• Extracting pitch from short noisy segment is
  difficult
• One approach is to maximize autocorrelation
• Periodicity isnt strong enough
• Threshold cant be used because maximum value not
  known in advance

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LPC - Estimating Pitch Period

• LPC-10 uses average magnitude difference function
  (AMDF)
• AMDF(P) (1/N)?yi-yi-P
• If yn is periodic with period P0, samples P0
  apart will have values close to each other and
  AMDF will have a min at P0
• AMDF is periodic for voiced and roughly flat for
  unvoiced
• AMDF is min when P is the pitch period and
  spurious min in unvoiced segments are shallow

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LPC - Obtaining Vocal Tract Filter

• At transmitter, we want filter coeffs that best
  match the segment in a mean squared error
• en2(yn- ?aiyn-iG?n)2
• Autocorrelation approach assumes yn is
  stationary
• A R-1P
• Recursive solution uses Levinson-Durbin

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LPC - Obtaining the Vocal Tract Filter

• Covariance approach discards stationarity
  assumption (not valid for speech signals)
• cij Eyn-iyn-j
• yields
• CA S

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LPC - Obtaining the Vocal Tract Filter

• cij are estimated as
• cij ?yn-iyn-j
• No longer assume values of yn outside of segment
  are zero
• Cholesky decomposition required
• Reflection coeffs used to update voicing decision

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LPC - Transmitting Parameters

• Tenth order filter used for voiced speech and
  fourth order for unvoiced
• Vocal tract filter is sensitive to errors in
  reflection coeffs close to one
• gi (1ki)/(1-ki)
• are quantized and sent instead of ki

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Code Excited Linear Prediction

• Single pulse per pitch period leads to buzzy
  twang
• Variety of excitation signals is allowed
• For each segment encoder finds excitation vector
  that generates synthesized speech that best
  matches speech being coded

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Sub-band adaptive filtering

• Multi-channel speech enhancement system
• Greater number of sub-bands used, the faster the
  convergence of the overall system

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Cochlear Modelling

• Sub-band filters are distributed logarithmically
  in frequency to approximate distribution of
  filters in cochlea

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Adaptive Noise Cancellation

• LMS algorithm is used to model differential
  transfer function between noise signals in a
  number of sub-bands
• Lower power and shorter filters used in each
  sub-band
• Convergence is equal across all bands if power is
  distributed equally and filter lengths are the
  same
• Convergence dominated by sub-band with greatest
  power