Signal Processing and Integrated Circuits

Chapter 8

Finite Word-length Effects in Digital Signal Processors

8.1 Introduction

We have seen that a digital filter, or a general digital signal processing system, operates on an input sampled-data signal to produce an output sampled-data signal by means of a computational algorithm. Since the sampled-data signals are represented by number sequences, these are quantized and encoded using binary codes, and the processor algorithm can be implemented either in software using a general purpose computer or in dedicated hardware. The latter approach is becoming increasingly popular due to the advances in very large scale intergration (VLSI) and the resulting availability of integrated circuit modules and special purpose hardward with sufficient memory size, complexity and speed so as to render the hardware implementation of digital filters, operating in real time, an attractive technique.

Now, regardless of the type of implementation, the numbers processed by the digital system are ultimately stored in (memory) registers with finite capacity. Therefore, all digital networks operate with only a finite number of binary digits (bits); thus resulting in an inherent limitation on the accuracy of processing. In this chapter, we discuss the affect of using finite word-lengths to represent the numbers and the arithmetic operations, on the accuracy of digital signal processors in general and digital filters in particular [12, 20].

The errors due to the use of finite word-lengths to represent ...