Feature Extraction for ASR
Spectral
(envelope)
Analysis
Auditory
Model/
Normalizations
Deriving the envelope (or
the excitation)
excitation
e(n)
Time-varying filter
ht(n)
y(n)=e(n)*ht(n)
HOW CAN WE GET e(n) OR h(n) from y(n)?
But first, why?
• Excitation/pitch: for vocoding; for synthesis; for signal
transformation; for prosody extraction (emotion, sentence
end, ASR for tonal languages …); for voicing category in
ASR
• Filter (envelope): for vocoding; for synthesis; for
phonetically relevant information for ASR
Spectral Envelope Estimation
• Filters
• Cepstral Deconvolution
(Homomorphic filtering)
• LPC
Channel vocoder
(analysis)
Broad w.r.t harmonics
e(n)*h(n)
Bandpass power estimation
Band-pass filter
A
B
Rectifier
Low-pass filter
A
B
C
C
Deriving spectral envelope
with a filter bank
BP 1
rectify
LP 1
decimate
BP 2
rectify
LP 2
decimate
Magnitude
signals
speech
BP N
rectify
LP N
decimate
Filterbank properties
• Original Dudley Voder/Vocoder: 10 filters,
300 Hz bandwidth (based on # fingers!)
• A decade later, Vaderson used 30 filters,
100 Hz bandwidth (better)
• Using variable frequency resolution, can use
16 filters with the same quality
Mel filterbank
• Warping function B(f) = 1125 ln (1 + f/700)
• Based on listening experiments with pitch
Towards other
deconvolution methods
• Filters seem biologically plausible
• Other operations could potentially
separate excitation from filter
• Periodic source provides harmonics
(close together in frequency)
• Filter provides broad influence
(envelope) on harmonic series
• Can we use these facts to separate?
“Homomorphic”
processing
• Linear processing is well-behaved
• Some simple nonlinearities also permit
simple processing, interpretation
• Logarithm a good example; multiplicative
effects become additive
• Sometimes in additive domain, parts more
separable
• Famous example: blind deconvolution of
Caruso recordings
IEEE Oral History Transcripts: Oppenheim on Stockham’s
Deconvolution of Caruso Recordings (1)
Oppenheim: Then all speech compression systems and many speech recognition systems are
oriented toward doing this deconvolution, then processing things separately, and then going on
from there. A very different application of homomorphic deconvolution was something that Tom
Stockham did. He started it at Lincoln and continued it at the University of Utah. It has become
very famous, actually. It involves using homomorphic deconvolution to restore old Caruso
recordings.
Goldstein: I have heard about that.
Oppenheim: Yes. So you know that's become one of the well-known applications of
deconvolution for speech.
…
Oppenheim: What happens in a recording like Caruso's is that he was singing into
a horn that to make the recording. The recording horn has an impulse response, and that
distorts the effect of his voice, my talking like this. [cupping his hands around his mouth]
Goldstein: Okay.
IEEE Oral History Transcripts (2)
Oppenheim: So there is a reverberant quality to it. Now what you want to do is deconvolve that
out, because what you hear when I do this [cupping his hands around his mouth] is the
convolution of what I'm saying and the impulse response of this horn. Now you could say, "Well
why don't you go off and measure it. Just get one
of those old horns, measure its impulse response, and then you can do the deconvolution."
The problem is that the characteristics of those horns changed with temperature, and they
changed with the way they were turned up each time. So you've got to estimate that from the
music itself. That led to a whole notion which I believe Tom launched, which is the concept of
blind deconvolution. In other words, being able to estimate from the signal that you've got the
convolutional piece that you want to get rid of. Tom did that using some of the techniques of
homomorphic filtering. Tom and a student of his at Utah named Neil Miller did some further
work. After the deconvolution, what happens is you apply some high pass filtering to the
recording. That's what it ends up doing. What that does is amplify some of the noise that's on
the recording. Tom and Neil knew Caruso's singing. You can use the homomorphic vocoder
that I developed to analyze the singing and then resynthesize it. When you resynthesize it you
can do so without the noise. They did that, and of course what happens is not only do you get
rid of the noise but you get rid of the orchestra. That's actually become a very fun demo which I
still play in my class. This was done twenty years ago, but it's still pretty dramatic. You hear
Caruso singing with the orchestra, then you can hear the enhanced version after the blind
deconvolution, and then you can also hear the result after you get rid of the orchestra,. Getting
rid of the orchestra is something you can't do with linear filtering. It has to be a nonlinear
technique.
Log processing
•
•
•
•
Suppose y(n) = e(n)*h(n)
Then Y(f) = E(f)H(f)
And logY(f) = log E(f) + log H(f)
In some cases, these pieces are
separable by a linear filter
• If all you want is H, processing can
smooth Y(f)
Source-filter separation by
cepstral analysis
Excitation
Windowed
speech
FFT
Log
magnitude
FFT
Pitch
detection
Time
Spectral
separation function
Cepstral features
•
•
•
•
Typically truncated (smoothing)
Corresponds to spectral envelope estimation
Features also are roughly orthogonal
Common transformation for many spectral
features, e.g.,
- filter bank energies
- FFT power
- LPC coefficients
• Used almost universally for ASR (in some form)
Key Processing Step for
ASR:
Cepstral Mean
Subtraction
• Imagine a fixed filter h(n), so y(n)=h(n)*x(n)
• Same arguments as before, but
- let x vary over time
- let h be fixed over time
• Then average cepstra should represent the
fixed component (including fixed part of x)
• (Think about it)
An alternative:
Incorporate Production
• Assume simple excitation/vocal tract model
• Assume cascaded resonators for vocal tract
frequency response (envelope)
• Find resonator parameters for best spectral
approximation
=
=
= r2
Some LPC Issues
• Error criterion
• Model order
LPC Peak Modeling
• Total error constrained to be (at best)
gain factor squared
• Error where model spectrum is larger
contributes less
• Model spectrum tends to “hug” peaks
LPC Spectrum
More effects of
error criterion
• Globally tracks, but worse match in
log spectrum for low values
• “Attempts” to model anti-aliasing
filter, mic response
• Ill-conditioned for wide-ranging spectral
values
Other LPC properties
• Behavior in noise
• Sharpness of peaks
• Speaker dependence
Model Order
• Too few, can’t represent formants
• Too many, model detail, especially harmonics
• Too many, low error, ill-conditioned matrices
LPC Model Order
Optimal Model Order
• Akaike Information Criterion (AIC)
• Cross-validation (trial and error)
Coefficient Estimation
• Minimize squared error - set derivs to zero
• Compute in blocks or on-line
• For blocks, use autocorrelation or covariance
methods (pertains to windowing, edge effects)
Solving the Equations
• Autocorrelation method: Levinson or Durbin
recursions, O(P2) ops; uses Toeplitz property
(constant along left-right diagonals),
guaranteed stable
• Covariance method: Cholesky decomposition,
O(P3) ops; just uses symmetry property, not
guaranteed stable
LPC-based representations
• Predictor polynomial - ai, 1<=i<=p , direct computation
• Root pairs - roots of polynomial, complex pairs
• Reflection coefficients - recursion; interpolated values
always stable (also called PARCOR coefficients ki, 1<=i<=p)
• Log area ratios = ln((1-k)/(1+k)) , low spectral sensitivity
• Line spectral frequencies - freq. pts around resonance;
low spectral sensitivity, stable
• Cepstra - can be unstable, but useful for recognition
Autocorrelation
Analysis
Spectral Estimation
Filter Banks
Reduced Pitch Effects
X
Excitation Estimate
Direct Access to Spectra
X
Less Resolution at HF
X
Orthogonal Outputs
Peak-hugging Property
Reduced Computation
Cepstral
Analysis
LPC
X
X
X
X
X
X
X
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