Robustness Stability Analysis of Higher-Order DPCM Prediction Filters

Abstract

This paper considers the robustness of the differential pulse-code modulation system with higher-order predictors. Special attention is paid to the robust parametric stability of the prediction filters with respect to the predictor coefficients. A generalisation of robustness in the classical sense is performed, and appropriate relations for calculating the probability of robustness are derived using Kharitonov principle. The proposed robustness estimation method is used for the third- and fourth-order prediction filters on speech signals, where the application of traditional methods is too difficult. For this reason, the Monte Carlo method is used to solve complex probability integrals. Verification and error analysis are performed for the previously considered second-order predictor. Satisfactory predetermined accuracy is achieved by increasing the number of samples. The results obtained could be very useful to design a system with suitable values for the predictor coefficients.

Keywords

• digital filters; linear feedback control systems; monte carlo methods; probability density function