December 2005
Intermediate to advanced
475 pages
12h 6m
English
Content preview from Signals and Systems
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SIGNIFICANT POINTS
The convolution of x(t) with h(t) is defined by
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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