Linear Convolution

The convolution gives the response y(n)  of the Linear Time Invariant System as a function of the input signal x(n) and the impulse response h(n).

Definition of the Linear convolution is :




The process can be summarized as follows:


Folding: Fold h(k) about k = 0 to obtain h(-k).

Shifting: Shift h(-k) by p to the right (left)  if p is positive (negative), to obtain h(p-k).

Multiplication: Multiply x(k) by  h(p-k) to obtain the product sequences as x(k)h(p-k).

Summation: sum all the values of the product sequences to obtain the values of the output.







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