If the input *x*(*n*) is given to discrete time system having an impulse {*h*(*n*)}, the output is given by convolving the {*h*(*n*)} with *x*(*n*).

where the symbol ‘*’ represents the convolution of *x*(*n*) with *h*(*n*) and this process is also called convolution sum. It is defined by

The limits will reduce to 0 to *n* for one-sided *x*(*n*) and *h*(*n*).

**Proof:**

Fig. 7.7 shows an inpu*t* sequence {*x*(*n*)}.

**Fig. 7.7** Input sequence {x(n)}

Let us express *x*(*n*) as a sum of delta sequences. We can write ...

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