Linear Prediction Coding of Speech Signal

Jun-Won Suh

What is Linear Prediction? Any random signal can be approximated

as a linear combination of past random signal samples

Estimate the basic speech parameters, like vocal tract area functions and articulator position

I can predict what will happen based on past events!

Where can I use this?

Oil industry used this method to find gas.

Random Signals

Economics (Stock Market)

How can I predict? Minimize the prediction error over a short

segment of the speech waveform, S(n)

Prediction error is defined by, e(n)

Error could neglected from center of distribution.

How can I predict?

Mean Square Error Weighted average of the squares

of the distances between n and k

Find the optimum value of αk

How can I solve αk faster? Based on differentiated MSE

Autocorrelation Method

Covariance Method

Autocorrelation Method

Autocorrelation : Rs(n) = E[ S(n) * S(n-k) ]

R is Toeplitz matrix :symmetric and all the elements along a given diagonal are

equal

Algorithm for Autocorrelation

Levinson Durbin Algorithm

Prediction error related to order of predictor. Reflection coefficient should be -1 to 1 to make

stable sysem. Each iteration all the coefficients are updated

Covariance Method

Covariance : C is positive definite symmetric

matrix. With this matrix property, use the

Cholesky decomposition method

Covariance Method

Cholesky decomposition procedure leads to a very simple expression for the minimum error predicton

α4 = Y4 / d4 α3 = Y3 / d3 – V43α4 α2 = Y2 / d2 – V32α3 - V42α4 α1 = Y1 / d1 – V21α2 - V31α3 -

V41α4

Comparison

Both methods are related to length of signal

CovarianceMethod

Autocorrelation Method

Memory N1 N2

MatrixMult.

N1P N2P

SolutionMult

P3 P2

Implementation

Pattern Recognition applethttp://www.cavs.msstate.edu/~suh/public_html/src

IFC of ISIP Prediction Classhttp://www.isip.msstate.edu/projects/speech/software/documentation

*IFC: ISIP Foundation Classes

Summary

Property of Linear system has great impact to compute solution.

Toeplitz MatrixCholesky Decompostion

N, length of signal within time interval, is trade off between computation time and quality of signal.

Question???