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Spectral envelope analysis of TIMIT corpus

Spectral envelope analysis of TIMIT corpus. using LP, WLSP, and MVDR. Steve Vest Matlab implementation of methods by Tien-Hsiang Lo. Overview. Methods WLSP MVDR TIMIT corpus Measurements. Analysis methods. LP Linear Prediction using autocorrelation method WLSP

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Spectral envelope analysis of TIMIT corpus

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  1. Spectral envelope analysis of TIMIT corpus using LP, WLSP, and MVDR Steve Vest Matlab implementation of methods by Tien-Hsiang Lo

  2. Overview • Methods • WLSP • MVDR • TIMIT corpus • Measurements

  3. Analysis methods • LP • Linear Prediction using autocorrelation method • WLSP • Weighted-sum Line Spectrum Pairs • MVDR • Minimum Variance Distortionless Response • MVDR of WLSP • MVDR applied to WLSP coefficients

  4. WLSP • Purpose: Increase spectral dynamics between peaks and valleys in spectral envelope • Maximizes difference between peak and valley amplitudes • Uses autocorrelation values beyond N to obtain better accuracy • When applied to Speech coding • Improves quality of decoded speech • Attenuates quantization noise level in the valleys

  5. WLSP Algorithm • Apply Hamming window to signal • Calculate N-1 order LP coefficients • Using LP coefficients calculate LSP polynomials where p and q are the symmetric and antisymmetric LSP polynomials, â is the zero-extended vector of LP coefficients, and âR is the reversal of â.

  6. WLSP Algorithm 3. Calculate WLSP polynomial 4. λ is the weighting parameter chosen to minimize the error between the autocorrelations of the speech and the WLSP all-pole filter impulse response • autocorrelations match n=1:N • Minimize SSE for n=N+1:N+1+L

  7. WLSP vs. LP

  8. MVDR • Estimates the power at each frequency by applying a special FIR filter • Distortionless constraint • FIR filter minimizes the total output power while preserving unity gain at the estimating frequency • Solving for distortionless filter is a constrained optimization problem • More robust modeling method than LP but can be equated from LP

  9. MVDR Algorithm • Calculate LP coefficients ak • Calculate MVDR coefficients μk Note that MVDR coefficients are symmetric and have order 2N+1

  10. MVDR vs. LP

  11. MVDR of WLSP • Just an exercise out of curiosity • Performs WLSP • Performs MVDR using coefficients from WLSP instead of LP • Resulting conclusion • It’s a bad idea…

  12. MVDR of WLSP vs. MVDR

  13. TIMIT corpus • “The TIMIT corpus of read speech has been designed to provide speech data forthe acquisition of acoustic-phonetic knowledge and for the development andevaluation of automatic speech recognition systems.” • Large collection of speech samples from 8 regions of the USA • Samples are phonetically labeled

  14. TIMIT regions • Region 1: New England • Region 2: Northern • Region 3: North Midland • Region 4: South Midland • Region 5: Southern • Region 6: New York City • Region 7: Western • Region 8: Army Brat (moved around)

  15. Analyzed Vowels • oy boy • ow boat • uh book • uw boot • ux toot • er bird • ax about • ix debit • axr butter • ax-h suspect • iy beet • ih bit • eh bet • ey bait • ae bat • aa bott • aw bout • ay bite • ah but • ao bought

  16. Collected Data • First three formants • Frequency [Hz] • Amplitude [dB] • Valleys after formants • Frequency [Hz] • Delta [dB] • Difference between formant amplitude and valley amplitude • Collected from entire training data set in TIMIT corpus

  17. Collected Data • Data organized by: • Vowel • Region • Sex • Spectral approximation method • Trineme • Phonemes preceding and following vowel

  18. Collected Data • Filter orders N=22 • LP: N → 22 • WLSP: M=N+1=23 • MVDR: M=2(2N)+1=89 • MVDR of WLSP: M=2(2N)+1=89 • WLSP data is erroneous • Hamming window was not applied which has noticeable impact on results • MVDR of WLSP needs to be excluded • MVDR order is too high

  19. General Observations • Formant locations vary greatly • Between different speakers • Between different Trinemes • 100-200 Hz for F1 • 300-600 Hz for F2 • 600-1000 Hz for F3

  20. Work still to be done • Optimize methods • e.g. WLSP search method for λ • Analysis of data took over 5 hrs • Determine best filter orders for each method • Reorganize data storage for easier analysis • Very difficult to sort through 100,000 sets of data averages • Determine exact statistics to be taken • Perform analysis of TIMIT data again

  21. Sources • Murthi, Manohar N. “All-Pole Modeling of Speech Based on the Minimum Variance Distortionless Response Spectrum”. IEEE Transactions on Speech and Audio Processing, Vol. 8, No. 3, May 2000 • Backstrom, Tom. “All-Pole Modeling Technique Based on Weighted Sum of LSP Polynomials”. IEEE Signal Processing Letters, Vol. 10, No. 6, June 2003

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