2 - Discrete Representation of Signals

Abstract

This chapter presents the representations of discrete signals and systems. An arbitrary discrete-time signal is expressed as a sequence of numbers using a weighted and time-shifted sum of unit impulses. It defines the linear and time-invariant discrete systems, and presents the convolution operation carried out between the impulse response sequence and input sequence. The chapter also provides a brief description of the Fourier series expansion of a periodic time sequence and presents the Fourier and Laplace transforms of transient time sequences. It also provides examples of Fourier transforms of several useful time sequences. Finally, the chapter describes the sampling process for continuous signals and the aliasing problem caused by sampling. The chapter describes the basic issues for processing continuous–time signals in a digital processor implemented with computer software and for hardware. It presents discrete expressions for signals in the time domain. The input–output relations of linear time-invariant discrete systems are shown using a unit impulse response (impulse response) sequence, and a convolution operation between an input sequence and the impulse response sequence is obtained.