Algorithms and Parallel Computing

9.1 INTRODUCTION

Many digital signal processing (DSP) algorithms are studied using the z-transform where the signals being considered are discrete time signals. A discrete time signal is denoted by x(n),where the variable n assumes nonnegative integer values 0, 1, … . The samples of a right-sided signal x are represented by the time sequence

(9.1)

The most common examples of these algorithms are found in digital filters such as one-dimensional (1-D) and multidimensional finite impulse response (FIR) filters and infinite impulse response (IIR) filters. We see examples of such algorithms also in multirate systems such as decimators, interpolators, and filter banks. z-Domain is used here to obtain different ways to implement a given algorithm using pipelines. The analysis in this chapter will proceed using as a working example the case of a 1-D FIR filter.