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Linear Prediction Coding of Speech Signal

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

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Linear Prediction Coding of Speech Signal

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  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 αk

  6. How can I solve αk faster? • Based on differentiated MSE • Autocorrelation Method • Covariance Method

  7. 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

  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

  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???

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