1. Linear Prediction Coding of Speech Signal Jun-Won Suh

2. 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!

3. Where can I use this? Oil industry used this method to find gas. Random Signals Economics (Stock Market)

4. 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.

5. How can I predict? Mean Square Error Weighted average of the squares of the distances between n and k Find the optimum value of α k

6. How can I solve α k faster? Based on differentiated MSE Autocorrelation Method Covariance Method

7. Autocorrelation Method Autocorrelation : R s (n) = E[ S(n) * S(n-k) ] R is Toeplitz matrix : symmetric and all the elements along a given diagonal are equal

8. 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

9. Covariance Method Covariance : C is positive definite symmetric matrix. With this matrix property, use the Cholesky decomposition method

10. 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

11. Comparison Both methods are related to length of signal Covariance Method Autocorrelation Method MemoryN1N1 N2N2 Matrix Mult. N1PN1PN2PN2P Solution Mult P3P3 P2P2

12. Implementation Pattern Recognition applet http://www.cavs.msstate.edu/~suh/public_html/src IFC of ISIP Prediction Class http://www.isip.msstate.edu/projects/speech/software/documentation *IFC: ISIP Foundation Classes

13. Summary Property of Linear system has great impact to compute solution. Toeplitz Matrix Cholesky Decompostion N, length of signal within time interval, is trade off between computation time and quality of signal.

14. Question???