Voice DSP Processing II

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VoiceDSPProcessing II

• Yaakov J. Stein
• Chief ScientistRAD Data Communications

2
Voice DSP

• Part 1 Speech biology and what we can learn from
  it
• Part 2 Speech DSP (AGC, VAD, features, echo
  cancellation)
• Part 3 Speech compression techiques
• Part 4 Speech Recognition

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Voice DSP - Part 2

• Simplest processing
• Gain
• AGC
• VAD
• More complex processing
• pitch tracking
• U/V decision
• computing LPC
• other features

• Echo Cancellation
• Sources of echo
• Echo suppression
• Echo cancellation
• Adaptive noise cancellation
• The LMS algorithm
• Other adaptive algorithms
• The standard LEC

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Voice DSP - Part 2a

• Simplest
• voice
• DSP

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Gain (volume) Control

• In analog processing (electronics) gain requires
  an amplifier
• Great care must be taken to ensure linearity!
• In digital processing (DSP) gain requires only
  multiplication
• y G x
• Need enough bits!

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Automatic Gain Control (AGC)

• Can we set the gain automatically?
• Yes, based on the signals Energy!
• E x2 (t) dt S xn2
• All we have to do is apply gain until attain
  desired energy
• Assume we want the energy to be Y
• Then
• y Y/ E x G x
• has exactly this energy

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AGC - cont.

• What if the input isnt stationary (gets stronger
  and weaker over time) ?
• The energy is defined for all times - lt t lt
• so it cant help!
• So we define energy in window E(t)
• and continuously vary gain G(t)
• This is Adaptive Gain Control
• We dont want gain to jump from window to window
• so we smooth the instantaneous gain
• G(t) a G(t) (1-a) Y/E(t)
• IIR filter

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8
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AGC - cont.

• The a coefficient determines how fast G(t) can
  change
• In more complex implementations we may separately
  control
• integration time, attack time, release time
• What is involved in the computation of G(t) ?
• Squaring of input value
• Accumulation
• Square root (or Pythagorean sum)
• Inversion (division)
• Square root and inversion are hard for a DSP
  processor
• but algorithmic improvements are possible (and
  often needed)

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Simple VAD

• Sometimes it is useful to know whether someone is
  talking (or not)
• Save bandwidth
• Suppress echo
• Segment utterances
• We might be able to get away with energy VOX
• Normally need Noise Riding Threshold / Signal
  Riding Threshold
• However, there are problems energy VOX
• since it doesnt differentiate between speech and
  noise
• What we really want is a speech-specific activity
  detector
• Voice Activity Detector

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Simple VAD - cont.

• VADs operate by recognizing that speech is
  different from noise
• Speech is low-pass while noise is white
• Speech is mostly voiced and so has pitch in a
  given range
• Average noise amplitude is relatively constant
• A simple VAD may use
• zero crossings
• zero crossing derivative
• spectral tilt filter
• energy contours
• combinations of the above

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Other simple processes

• Simple not significantly dependent on details
  of speech signal
• Speed change of recorded signal
• Speed change with pitch compensation
• Pitch change with speed compensation
• Sample rate conversion
• Tone generation
• Tone detection
• Dual tone generation
• Dual tone detection (need high reliability)

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Voice DSP - Part 2b

• Complex
• voice
• DSP

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Correlation

• One major difference between simple and complex
  processing
• is the computation of correlations (related to
  LPC model)
• Correlation is a measure of similarity
• Shouldnt we use squared difference to measure
  similarity?
• D2 lt (x(t) - y(t) )2 gt
• No, since squared difference is sensitive to
• gain
• time shifts

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Correlation - cont.

• D2 lt (x(t) - y(t) )2 gt lt x2 gt lt y2 gt
  - 2 lt x(t) y(t) gt
• So when D2 is minimal C(0) lt x(t) y(t) gt is
  maximal
• and arbitrary gains dont change this
• To take time shifts into account
• C(t) lt x(t) y(tt) gt
• and look for maximal t !
• We can even find out how much a signal resembles
  itself

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Autocorrelation

• Crosscorrelation Cx y (t) lt x(t) y(tt) gt
• Autocorrelation Cx (t) lt x(t) x(tt) gt
• Cx (0) is the energy!
• Autocorrelation helps find hidden periodicities!
• Much stronger than looking in the time
  representation
• Wiener Khintchine
• Autocorrelation C(t) and Power Spectrum S(f) are
  FT pair
• So autocorrelation contains the same information
  as the power spectrum
• and can itself be computed by FFT

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Pitch tracking

• How can we measure (and track) the pitch?
• We can look for it in the spectrum
• but it may be very weak
• may not even be there (filtered out)
• need high resolution spectral estimation
• Correlation based methods
• The pitch periodicity should be seen in the
  autocorrelation!
• Sometimes computationally simpler is the
• Absolute Magnitude Difference Function
• lt x(t) - x(tt) gt

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Pitch tracking - cont.

• Sondhis algorithm for autocorrelation-based
  pitch tracking
• obtain window of speech
• determine if the segment is voiced (see U/V
  decision below)
• low-pass filter and center-clip
• to reduce formant
  induced correlations
• compute autocorrelation lags corresponding to
  valid pitch intervals
• find lag with maximum correlation OR
• find lag with maximal accumulated correlation in
  all multiples
• Post processing
• Pitch trackers rarely make small errors (usually
  double pitch)
• So correct outliers based on neighboring values

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Other Pitch Trackers

• Millers data-reduction Gold and Rabiners
  parallel processing methods
• Zero-crossings, energy, extrema of waveform
• Nolls cepstrum based pitch tracker
• Since the pitch and formant contributions are
  separated in cepstral domain
• Most accurate for clean speech, but not robust in
  noise
• Methods based on LPC error signal
• LPC technique breaks down at pitch pulse onset
• Find periodicity of error by autocorrelation
• Inverse filtering method
• Remove formant filtering by low-order LPC
  analysis
• Find periodicity of excitation by autocorrelation
• Sondhi-like methods are the best for noisy speech

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U/V decision

• Between VAD and pitch tracking
• Simplest U/V decision is based on energy and zero
  crossings
• More complex methods are combined with pitch
  tracking
• Methods based on pattern recognition
• Is voicing well defined?
• Degree of voicing (buzz)
• Voicing per frequency band (interference)
• Degree of voicing per frequency band

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LPC Coefficients

• How do we find the vocal tract filter
  coefficients?
• System identification problem
• All-pole (AR) filter
• Connection to prediction
• Sn G en Sm am sn-m
• Can find G from energy (so lets ignore it)

Unknown filter
known input
known output
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LPC Coefficients

• For simplicity lets assume three a coefficients
• Sn en a1 sn-1 a 2 s n-2 a 3 s
  n-3
• Need three equations!
• Sn en a1 sn-1 a 2 s n-2
  a 3 s n-3
• Sn1 en1 a1 sn a 2 s n-1 a
  3 s n-2
• Sn2 en2 a1 sn1 a 2 s n a 3
  s n-1
• In matrix form
• Sn en sn-1 s
  n-2 s n-3 a1
• Sn1 en1 sn s n-1
  s n-2 a 2
• Sn2 en2 sn1 s n
  s n-1 a 3
• s e S a

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LPC Coefficients - cont.

• S e S a
• so by simple algebra
• a S-1 ( s - e )
• and we have reduced the problem to matrix
  inversion
• Toeplitz matrix so the inversion is easy
  (Levinson-Durbin algorithm)
• Unfortunately noise makes this attempt break
  down!
• Move to next time and the answer will be
  different.
• Need to somehow average the answers
• The proper averaging is before the equation
  solving
• correlation vs autocovariance

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LPC Coefficients - cont.

• Cant just average over time - all equations
  would be the same!
• Lets take the input to be zero
• Sn Sm am sn-m
• multiply by Sn-q and sum over n
• Sn Sn Sn-q Sm am Sn sn-m sn-q
• we recognize the autocorrelations
• Cs (q) Sm Cs (m-q) am
• Yule-Walker equations
• autocorrelation method sn outside window are
  zero (Toeplitz)
• autocovariance method use all needed sn (no
  window)
• Also - pre-emphasis!

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Alternative features

• The a coefficients arent the only set of
  features
• Reflection coefficients (cylinder model)
• log-area coefficients (cylinder model)
• pole locations
• LPC cepstrum coefficients
• Line Spectral Pair frequencies
• All theoretically contain the same information
  (algebraic transformations)
• Euclidean distance in LPC cepstrum space
  Itakura Saito measure
• so these are popular in speech recognition
• LPC (a) coefficients dont quantize or
  interpolate well
• so these arent good for speech compression
• LSP frequencies are best for compression

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LSP coefficients

• a coefficients are not statistically equally
  weighted
• pole positions are better (geometric)
• but radius is sensitive near unit circle
• Is there an all-angle representation?
• Theorem 1 Every real polynomial with all roots
  on the unit circle
• is palindromic (e.g. 1 2t t2) or
  antipalindromic (e.g. t t2 - t3)
• Theorem 2 Every polynomial can be written as the
  sum of
• palindromic and antipalindromic polynomials
• Consequence Every polynomial can be represented
  by roots
• on the unit circle, that is, by angles

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Voice DSP - Part 2c

• Echo
• Cancellation

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Acoustic Echo
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Line echo
hybrid
hybrid
Telephone 1
Telephone 2
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Echo suppressor

In practice need more VOX, over-ride, reset, etc.
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Why not echo suppresion?

• Echo suppression makes conversation half duplex
• Waste of full-duplex infrastructure
• Conversation unnatural
• Hard to break in
• Dead sounding line
• It would be better to cancel the echo
• subtract the echo signal allowing desired signal
  through
• but that requires DSP.

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Echo cancellation?

• Unfortunately, its not so easy
• Outgoing signal is delayed, attenuated, distorted
• Two echo canceller architectures
• MODEM TYPE
• LINE ECHO CANCELLER (LEC)

-
echo path
near end
far end
clean
clean
-
near end
far end
echo path
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LEC architecture

h y b r i d
A/D
NLP
-
Y
filter H
doubletalk detector
adapt
near end
far end
X
D/A
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Adaptive Algorithms

• How do we
• find the echo cancelling filter?
• keep it correct even if the echo path parameters
  change?
• Need an algorithm that continually changes the
  filter parameters
• All adaptive algorithms are based on the same
  ideas
• (lack of corellation between desired signal and
  interference)
• Lets start with a simpler case - adaptive noise
  cancellation

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Noise cancellation
y
h n
x
e n
y
x
-
n
h
e
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Noise cancellation - cont.

• Assume that noise is distorted only by unknown
  gain h
• We correct by transmitting e n so that the
  audience hears
• y x h n - e n x (h-e) n
• the energy of this signal is
• Ey lt y2 gt lt x2 gt (h-e)2 lt n2 gt 2 (h-e) lt
  x ngt
• Assume that Cxn lt x ngt 0
• We need only set e to minimize Ey ! (turn knob
  until minimal)
• Even if the distortion is a complete filter h
• we set the ANC filter e to minimize Ey

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The LMS algorithm

• Gradient descent on energy
• correction to H is proportional to error d times
  input X

H H l d X
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Nonlinear processing

• Because of finite numeric precision
• the LEC (linear) filtering can not completely
  remove echo
• Standard LEC adds center clipping to remove
  residual echo
• Clipping threshold needs to be properly set by
  adaptation

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Doubletalk detection

• Adaptation of H should take place only when far
  end speaks
• So we freeze adaptation when no far end or
  double-talk,
• that is whenever near end speaks
• Geigel algorithm compares absolute value of
  near-end speech
• to half the maximum absolute value in X buffer
• If near-end exceeds far-end can assume only
  near-end is speaking