Feature Extraction for speech applications

1. Feature Extraction for speech applications Chapters 19-22

2. The course so far • Brief introduction to speech analysis andrecognition for humans and machines • Some basics on speech production, acoustics,pattern classification, speech units

3. Where to next • Multi-week focus on audio signal processing • Start off with the “front end” for ASR • Goal: generate features good for classification • Waveform is too variable • Current front ends make some sense in termsof signal characteristics alone (productionmodel) - recall the spectral envelope • But analogy to perceptual system is there too • A bit of this now (much more on ASR in April)

4. Biological analogy • Essentially all ASR front ends start witha spectral analysis stage • “Output” from the ear is frequency dependent • Target-probe experiments going back toFletcher (remember him?) suggest a “critical band” • Other measurements also suggest similarmechanism (linear below 1kHz, log above)

7. Basic Idea (Fletcher) • Look at response to pure tone in white noise • Set tone level to just audible • Reduce noise BW, initially same threshold • For noise BW below critical value, audibilitythreshold goes down • Presence or absence of tone based on SNRwithin the band

8. Feature Extraction for ASR Spectral (envelope)Analysis AuditoryModel/Normalizations

9. Deriving the envelope (or the excitation) excitation Time-varying filter ht(n) e(n) y(n)=e(n)*ht(n) HOW CAN WE GET e(n) OR h(n) from y(n)?

10. 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 • Frequency dependency appears to be a key aspect of a system that works - human audition

11. Spectral Envelope Estimation • Filters • Cepstral Deconvolution (Homomorphic filtering) • LPC

13. Channel vocoder (analysis) Broad w.r.t harmonics e(n)*h(n)

14. Bandpass power estimation B C A Rectifier Band-pass filter Low-pass filter A B C

15. 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 decimate LP N

17. 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 use16 filters with the same quality

18. Mel filterbank • Warping function B(f) = 1125 ln (1 + f/700) • Based on listening experiments with pitch(mel is for “melody”)

19. Other warping functions • Bark(f) = [26.8 /(1 + (1960/f))] - 0.53 • (named after Barkhausen, proposed loudness scale) • Based on critical band estimates from masking • experiments • ERB(f) = 21.4 log10(1+ 4.37f/1000) • (Equivalent Rectangular Bandwidth)Similarly based on masking experiments,but with better estimates of auditory filter shape

20. All together now

21. 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?

22. “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

23. 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.

24. 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.

25. 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)

27. Source-filter separation by cepstral analysis Excitation Pitch detection Windowed speech Time separation Log magnitude Spectral function FFT FFT

28. Cepstral features • Typically truncated (smooths the estimate; why?) • Corresponds to spectral envelope estimation • Features also are roughly orthogonal • Common transformation for many spectral features • Used almost universally for ASR (in some form) • To reconstruct speech (without min phase assumption) need complex cepstrum

29. An alternative: Incorporate Production • Assume simple excitation/vocal tract model • Assume cascaded resonators for vocal tractfrequency response (envelope) • Find resonator parameters for best spectralapproximation

30. Resonator frequency response

31. Pole-only (complex) resonator Where r = pole magnitude, θ = pole angle

35. Error Signal where

37. Some LPC Issues • Error criterion • Model order

38. Error Criterion

39. LPC Peak Modeling • Total error constrained to be (at best)gain factor squared • Error where model spectrum is largercontributes less • Model spectrum tends to “hug” peaks

40. LPC spectra and error

41. More effects of LPC error criterion • Globally tracks, but worse match inlog spectrum for low values • “Attempts” to model anti-aliasingfilter, mic response • Ill-conditioned for wide-ranging spectralvalues

42. Other LPC properties • Behavior in noise • Sharpness of peaks • Speaker dependence

43. LPC Model Order • Too few, can’t represent formants • Too many, model detail, especially harmonics • Too many, low error, ill-conditioned matrices

44. LPC Speech Spectra

45. LPC Prediction error

46. Optimal Model Order • Akaike Information Criterion (AIC) • Cross-validation (trial and error)

47. 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)

48. Minimizing the error criterion If we take partial derivatives with respect to each for Where is a correlation sum between versions of the signal delayed by i and j points

49. 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

50. 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