Page 87 - DSP Integrated Circuits

72 Chapter 3 Digital Signal Processing

A causal system, as illustrated in Figure 3.11, is denned by

Figure 3.11 Input and output signals for a causal system

then for a causal system

For a causal LSI system the impulse response h(n) = 0 for n < 0 (see Problem
3.9). Note that noncausal systems can be used in practice in non-real-time
applications.

3.8.5 Stable LSI Systems
An LSI system is said to be stable in the bounded-input bounded-output sense
(BIBO)ifandonlyif

This is only a weak form of stability. In Chapter 5, we will show that the issue
of stability is more complicated than indicated by Equation (3.10). The poles,
which will be discussed in section 3.11, of an LSI system are confined within the
unit circle in the z-plane.

3.9 DIFFERENCE EQUATIONS

Many discrete-time and digital systems such as digital filters can be described by
difference equations with constant coefficients. The input-output relation for an
Afth-order LSI system can be described by