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Landmark-Based Speech Recognition: Spectrogram Reading, Support Vector Machines, Dynamic Bayesian Networks, and Phonolog

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### Landmark-Based Speech Recognition:Spectrogram Reading,Support Vector Machines,Dynamic Bayesian Networks,and Phonology

Mark Hasegawa-Johnson

University of Illinois at Urbana-Champaign, USA

Lecture 6: Speech Recognition Acoustic & Auditory Model Features

- Log spectral features: log FFT, cepstrum, MFCC
- Time-domain features: energy, zero crossing rate, autocorrelation
- Model-based features: LPC, LPCC, PLP
- Modulation filtering: cepstral mean subtraction, RASTA
- Auditory model based features: auditory spectrogram, correlogram, summary correlogram

The “Complex Cepstrum”

Cepstrum = Even Part of Complex Cepstrum

Euclidean Distance Between Two Spectra = Cepstral Distance…

… but Windowed Cepstral Distance = Distance Between Smoothed Spectra

The Bark Scale (a.k.a. “Critical Band Scale”): Noise Within 1 Bark Can “Mask” a Tone

Mel-Scale Spectra of Music(Petruncio, B.S. Thesis University of Illinois, 2003)

Piano

Saxophone

Tenor

Opera

Singer

Drums

“Time-Domain Features” = Features that can be computed frequently (e.g., once/millisecond)

- Energy-based features: energy, sub-band energies
- Low-order cepstral features: energy, spectral tilt, spectral centrality
- Zero-crossing rate
- Spectral flatness
- Autocorrelation

Example: 3 Features/1ms(Niyogi and Burges, 2002)

Waveform

Energy

HF Energy

Spectral Flatness

Stop-Detection SVM

TargetOutput

Figure from Niyogi & Burges, 2002

Energy-Based Features

- Filter the signal, to get the desired band
- [0,400]: is the signal voiced? (doesn’t work for telephone speech)
- [300,1000]: is the signal sonorant?
- [1000,3000]: distinguish nasals from glides
- [2000,6000]: detect frication energy
- Full Band (no filtering): syllable detection
- Window with a short window (4-6ms in length)
- Compute the energy:

Cepstrum-Based Features

- Average(log(energy)) = c[0]
- c[0] = ʃ log|X(w)|dw = ½ ʃ log |X(w)|2 dw
- Not the same as log(average(energy)), which is log ʃ |X(w)|2dw
- Spectral Tilt: one measure is -c[1]
- -c[1] = -ʃ log|X(w)|cos(w)dw ≈ HF log energy – LF log energy
- A More Universally Accepted Measure:
- Spectral Tilt = ʃ (w-p/2) log|X(w)| dw
- Spectral Centrality: -c[2]
- c[2] = -ʃ log|X(w)|cos(2w)dw
- c[2]≈ Mid Frequency Energy (p/4 to 3p/4) – Low and High Frequency Energy (0 to p/4 and 3p/4 to p)

Measures of Turbulence

- Zero Crossing Rate:
- Count the number of times that the signal crosses zero in one window. Many: frication. Some: sonorant. Few: silence.
- A related measure, used often in speech coding: “alternation rate” = the number of times the derivative crosses zero
- Spectral Flatness:
- average(log(energy)) – log(average(energy))
- Equal to zero if spectrum is flat (white noise, e.g., frication)
- Negative if spectrum is peaky (e.g., vowels)

Autocorrelation

- Autocorrelation: measures the similarity of the signal to a delayed version of itself
- Sonorant (low-frequency) signals: R[1] is large
- Fricative (high-frequency) signals: R[1] is small or negative
- R[0] is the energy
- -R[0] ≤ R[k] ≤ R[0] for all k

During Vowels and Glides, VT Transfer Function is All-Pole(All-Pole Model sometimes OK at other times too)

Finding LPC Coefficients: Solve the “Normal Equations”

- LPC Filter Prediction of s[n] is Saks[n-k]. Error is En:
- ak minimize the error if they solve the Normal Equations:

Roots of the LPC Polynomial

- Roots of the LPC Polynomial:
- Roots include:
- Complex pole pair at most formant frequencies, rk and rk*
- In a vowel or glide, there are additional poles at zero frequency:
- One or two with bandwidth ≈ 100-300Hz; these give a negative tilt to the entire spectrum
- One or two with bandwidth ≈ 2000-3000Hz; these attenuate high frequencies
- In a fricative: poles may be at w=p, causing the whole spectrum to be high-pass

Reflection Coefficients

- LPC Speech Synthesis Filter can be implemented using a reflection line. This reflection line is mathematically equivalent to a p-tube model of the vocal tract:
- PARCOR coefficients (= reflection coefficients) are found using the Levinson-Durbin recursion:

LAR and LSF

- Log Area Ratio (LAR) is bilinear transform of the reflection coefficients:
- Line Spectral Frequencies (LSF) are the resonances of two lossless vocal tract models. Set U(0,jW)=0 at glottis; result is P(z). Set P(0,jW)=0 at glottis, result is Q(z).

(Hasegawa-Johnson, JASA 2000)

LSFs Tend to Track Formants

- When LPC finds the formants (during vowels), the roots of P(z) and the roots of Q(z) each tend to “bracket” one formant, with a Q(z) root below, and a P(z) root above.
- When LPC can’t find the formants (e.g., aspiration), LSFs interpolate between neighboring syllables

Perceptual LPC(Hermansky, J. Acoust. Soc. Am., 1990)

- First, warp the spectrum to a Bark scale:
- The filters, Hb(k), are uniformly spaced in Bark frequency. Their amplitudes are scaled by the equal-loudness contour (an estimate of how loud each frequency sounds):

Perceptual LPC

- Second, compute the cube-root of the power spectrum
- Cube root replaces the logarithm that would be used in MFCC
- Loudness of a tone is proportional to cube root of its power

Y(b) = S(b)0.33

- Third, inverse Fourier transform to find the “Perceptual Autocorrelation:”

Perceptual LPC

- Fourth, use Normal Equations to find the Perceptual LPC (PLP) coefficients:
- Fifth, use the LPC Cepstral recursion to find Perceptual LPC Cepstrum (PLPCC):

Reverberation

- Reverberation adds echos to the recorded signal:
- Reverberation is a linear filter:

x[n] = Sk=0∞ak s[n-dk]

- If ak dies away fast enough (ak≈0 for dk>N, the STFT window length), we can model reverberation in the STFT frequency domain:

X(z) = R(z) S(z)

- Usually, STFT frequency-domain modeling of reverberation works for
- Electric echoes (e.g., from the telephone network)
- Handset echoes (e.g., from the chin of the speaker)
- But NOT for free-field echoes (e.g., from the walls of a room, recorded by a desktop microphone)

Cepstral Mean Subtraction: Subtract out Short-Term Reverb

- Log Magnitude Spectrum: Constant Filter → Constant Additive Term
- Reverberation R(z) is Constant during the whole sentence
- Therefore: Subtract the average value from each frame’s cepstrum log R(z) is completely subtracted away
- Warning: if the utterance is too short (contains too few phonemes), CMS will remove useful phonetic information!

Modulation Filtering

- Short-Time Log-Spectrum, log|Xt(w)|, is a function of t (frame number) and w.
- Speaker information (log|Pt(w)|), Transfer function information (log|Tt(w)|), and Channel/Reverberation Information (log|Rt(w)|) may vary at different speeds with respect to frame number t.

log|Xt(w)| = log|Rt(w)| + log|Tt(w)| + log|Pt(w)|

- Assumption: Only log|Tt(w)| carries information about phonemes. Other components are “noise.”
- Wiener filtering approach: filter log|Xt(w)| to compute an estimate of log|Tt(w)|.

log|Tt*(w)| = Sk hk log|Xt-k(w)|

RASTA (RelAtive SpecTral Amplitude)(Hermansky, IEEE Trans. Speech and Audio Proc., 1994)

- Modulation-filtering of the cepstrum is equivalent to modulation-filtering of the log spectrum:

ct*[m] = Sk hk ct-k[m]

- RASTA is a particular kind of modulation filter:

Processing of Sound by the Inner Ear

- Bones of the middle ear act as an impedance matcher, ensuring that not all of the incoming wave is reflected from the fluid-air boundary at the surface of the cochlea.
- The basilar membrane divides the top half of the cochlea (scala vestibuli) from the bottom half (scala tympani). The basal end is light and stiff, therefore tuned to high frequencies; the apical end is loose and floppy, therefore tuned to low frequencies. Thus the whole system acts like a bank of mechanical bandpass filters, with Q=centerfrequency/bandwidth≈6.
- Hair cells on the surface of the basilar membrane release neurotransmitter when they are bent down, but not when they are pulled up. Thus they half-wave rectify the wave-like motion of the basilar membrane.
- Neurotransmitter, in the cleft between hair cell and neuron, takes a little while to build up or to dissipate. The inertia of neurotransmitter acts to low-pass filter the half-wave rectified signal, with a cutoff around 2kHz. Result is a kind of localized energy in a ~0.5ms window.

Filtering: Different Frequencies Excite Different Positions on the Basilar Membrane

Inner and Outer Hair Cells on the Basilar Membrane. Each column of hair cells is tuned to a slightly different center frequency.

Half-Wave Rectification: Only Down-Bending of the Hair Cells Excites a Neural Response

Close-up view of outer hair cells, in a “V” configuration

Temporal Structure of the Neural Response

- Neural response patterns carries more information than just average energy (spectrogram)
- For example: periodicity
- Correlogram (Licklider, 1951): Measure periodicity on each simulated neuron by computing its autocorrelation
- Recursive Neural Net (Cariani, 2000): Measure periodicity by building up response strength in an RNN with different delay loops
- YIN pitch tracker (de Cheveigne and Kawahara, 2002): Measure periodicity using the absolute value of the difference between delayed signals

Correlogram of a Sine Wave: Center Frequency vs. Autocorrelation Delay, Snapshot at one Instant in Time

Correlogram of a Periodic Signalwith spectral peaks at 2F0, 3F0, etcetera but none at F0 (missing fundamental)

Correlogram of an Owl Hooting

- Y axis = neuron’s center frequency
- X axis = autocorrelation delay (same as on previous two slides
- Time = time lapsed in the movie (real-time movie)
- Notice: pitch fine structure, within each band, could be used to separate two different audio input signals, performing simultaneous recognition of two speech signals.

Summary

- Log spectrum, once/10ms, computed with a window of about 25ms, seems to carry lots of useful information about place of articulation and vowel quality
- Euclidean distance between log spectra is not a good measure of perceptual distance
- Euclidean distance between windowed cepstra is better
- Frequency warping (mel-scale or Bark-scale) is even better
- Fitting an all-pole model (PLP) seems to improve speaker-independence
- Modulation filtering (CMS, RASTA) improve robustness to channel variability (short-impulse-response reverb)
- Time-domain features (once/1ms) can capture important information about manner of articulation and landmark times
- Auditory model features (correlogram, delayogram) are useful for recognition of multiple simultaneous talkers

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