Spectral envelope analysis of TIMIT corpususing 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

ˆ ˆ

ˆ ˆR

Rp = a +a

q = a a

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.

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

1

0,1

d p q

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 ak

2. Calculate MVDR coefficients μk

*

0

*

11 2 , for 0 :

, for : 1

N k

i i kiek

k

N k i a a k NP

k N

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 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

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• iy beet• ih bit• eh bet• ey bait• ae bat• aa bott• aw bout• ay bite• ah but• ao

bought

• oy boy• ow boat• uh book• uw boot• ux toot• er bird• ax about• ix debit• axr butter• ax-h suspect

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• 100-200 Hz for F1• 300-600 Hz for F2• 600-1000 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