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3.8 Signal Processing Systems 71

where the impulse response is denoted by h(ri). The impulse response of a system is
obtained when the input signal is an impulse sequence, 80i).

EXAMPLE 3.3

We have

Hence

Instead of computing the convolution, it is often simpler to first compute the
product of the ^-transforms of the impulse response and the input sequence, and then
compute the inverse z-transform of Y(z). The properties of the system, which are rep-
resented by H(z), are separated in the z-domain from the properties of the input sig-
nal. Hence, we can analyze an LSI system without considering the input signal.

Another important property of LSI systems is that the order of two cascaded
LSI systems can be changed, as shown in Figure. 3.10 (see Problem 3.10). This fact
will allow us to rearrange the ordering of both DSP building blocks and certain
arithmetic operations in order to obtain favorable computational properties.

Figure 3.10 Changing the ordering of two LSI systems

3.8.4 Causal Systems
a
A system is causal, if the output signal, y(«o) t the time instant HQ, depends only
on the input signal for time values n < JIQ.