# DIGITAL SIGNAL AND SYSTEM

#### INTRODUCTION OF DIGITAL SIGNAL AND SYSTEM :

THE STUDYOF “SIGNALSAND SYSTEMS” hasformed a cornerstone forthe development of digital signal processing and is crucial for all of the topics discussed in this Handbook. While the reader is assumed to be familiar with the basics of signals and systems, a small portion is reviewed in this chapter with an emphasis on the transition from continuous time to discrete time.
The reader wishing more background may find in it any of the many fine textbooks in this area.

In the chapter “Fourier Series, Fourier Transforms, and the DFT” by W. Kenneth Jenkins, many important Fourier transform concepts in continuous and discrete time are presented. The discrete Fourier transform (DFT), which forms the backbone of modern digital signal processing as its most common signal analysis tool, is also described, together with an introduction to the fast Fourier transform algorithms.

In “Ordinary Linear Differential and Difference Equations”, the author, B.P. Lathi, presents a detailed tutorial of differential and difference equations and their solutions.

Because these equations are the most common structures for both implementing and modelling systems, this background is necessary for the understanding of many of the later topics in this Handbook. Of particular interest are a number of solved examples that illustrate the solutions to these formulations.

While most software based on workstations and PCs is executed in single or double precision arithmetic, practical realizations for some high throughput DSP applications must be implemented in fixed point arithmetic. These low cost implementations are still of interest to a wide community in the consumer electronics arena.

The chapter “Finite Wordlength Effects” by Bruce W. Bomar describes basic number representations, fixed and floating point errors, roundoff noise, and practical considerations for realizations of digital signal processing applications, with a special emphasis on filtering.