• Convolution is a mathematical operation which is used as a tool by communication engineers for system analysis , probability and transform calculations

• Convolution can be performed in time as well as frequency domain.

• The convolution of two function x (t) and y (t) is defined as,

• Equation (1) is called as convolution integral.

• The independent variable here is “t” which is same as the independent of the function x (t) and y (t) which are being convolved.

• The integration is always performed with respect to a dummy variable such as $τ$ .And t is treated as a constant so far as the integration is concerned.

• The process of convolution involves following operations of y ($τ$) while the signal

x ($τ$) remains unchanged:

1.Folding or time reversal to obtain y (-$τ$).

2.Time shifting the folded signal y (-$τ$) to obtain y(t- $τ$).

3.Multiplication of x (τ) and y (t-$τ$)

4.Integration of the product term x (τ) . y (t- $τ$)

• Convolution is practically used to obtain the response (output) y (t) of a system when input x (t) is applied to it.

• h (t) is the impulse response of the system. The output is equal to the convolution of x (t) and h (t).

• Therefore, Output y (t) = x (t)*h (t) .This is the practical use of convolution.