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 Weighted-sum Line Spectrum Pairs MVDR Minimum Variance Distortionless Response MVDR of WLSP MVDR applied to WLSP coefficients

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

WLSP Algorithm 1.Apply Hamming window to signal 2.Calculate N-1 order LP coefficients 3.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 â R is the reversal of â.

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

WLSP vs. LP

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

MVDR Algorithm 1.Calculate LP coefficients a k 2.Calculate MVDR coefficients μ k Note that MVDR coefficients are symmetric and have order 2N+1

MVDR vs. LP

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…

MVDR of WLSP vs. MVDR

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

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)

Analyzed Vowels iybeet ihbit ehbet eybait aebat aabott awbout aybite ahbut aobought oyboy owboat uhbook uwboot uxtoot erbird axabout ixdebit axrbutter ax-hsuspect

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

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

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

General Observations Formant locations vary greatly Between different speakers Between different Trinemes Hz for F Hz for F Hz for F3

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

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