Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 72. Autoregressive Processes and Linear Prediction Analysis

Linear prediction is a topic that is closely related to the generation of an autoregressive (AR) process. Techniques developed for linear prediction yield results that can be used in autoregressive modeling. Forward linear prediction estimates the value of the sample, x[n], as a weighted combination of the m previously observed samples, x[n –1] through x[n –m]

72.1

where the “hat” notation is used to distiguish estimated values, and the superscript f is used to indicate forward prediction. An FIR filter corresponding to Eq. (72.1) is shown in Figure 72.1. Of course, when the estimated ...