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Signals and Systems by Smarajit Ghosh

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SIGNIFICANT POINTS

 

The convolution of x(t) with h(t) is defined by

 

image

 

Properties of linear convolution:

Commutative Property:         x1(t)*x2(t) = x2(t)*x1(t)

Associative Property:      x1(t)*[x2(t) *x3(t)] = [x1(t)*x2(t)] *x3(t)

Distributive Property:   x1(t)*[x2(t) + x3(t)] = x1(t)*x2(t) + x1(t) *x3(t)

Discrete convolution:

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).

 

y(n) = h(n)*x(n) = x(n)*h(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 ...

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