The Probability of Stability Estimation of an Arbitrary Order DPCM Prediction Filter: Comparison Between the Classical Approach and the Monte Carlo Method
This paper presents the stability analysis of the linear recursive (prediction) filters with higher order predictors in a DPCM (differential pulse-code modulation) system, where traditional methods become too difficult and complex. Stability conditions for the third- and fourth-order predictor are given by using the Schur–Cohn stability criterion. The probability of stability estimation is performed by using the Monte Carlo method. Verification of the proposed method is performed for lower order predictors (the first- and second-order). We calculated numerical values of the probability of stability for higher order predictors and previously experimentally obtained parameters. With large enough number of trials (samples) in Monte Carlo simulation, we reach the desired accuracy.