Convolution of Signals 

Objective 

The objective of this experiment is to  convolve   two signals x(t) and h(t) to produce the output signal y(t) and to understand the concept of Linear and circular convolution and their properties.

Theory and Operation of Convolution

Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response. Convolution is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response 

Convolution Sum

Convolution of Finite Sequences 

Run the code below. Change the Input Sequence , Impulse Response and observe the output sequence. Explore and understand  how Linear convolution and circular convolution differs from each other.

Linear Convolution of Signals

Let us take the following signals:

• Input is square pulse of Duration 1

• Impulse response is again Square pulse of duration 1

Then computing  convolution of these two will produce the triangular pulse as shown below

One more example:

• Input is square pulse of Duration 1

• Impulse response is decaying exponential  1

Then computing  convolution of these two will produce the triangular pulse as shown below