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Signals and Systems by Smarajit Ghosh

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6.22 SYSTEM FUNCTION OF THE LTI SYSTEM

The output of a relaxed LTI system is given by

 

image

 

where y(n) is the output of the LTI system, x(n) is the input of LTI system and h(n) is the impulse response of the system. The output is the convolution of input and impulse response.

Let image be the z-transform pairs.

From Eq. (6.79), we can write after taking z-transform,

 

Y(z) = Z{x(n)*h(n)}

 

Using convolution property we can write that

 

Y(z) = X(z)H(z)     (6.81)

 

 

In Eq. (6.82) H(z) is known as system function which is the z-transform of the unit ...

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