One of the most important operation in signals processing is convolution. For a typical LTI system, the output can be produced by convolving the input with the given impulse responses. In general, we have 2 types of convolutions:
- Convolution sum for Discrete LTI system
- Convolution Integral for Continuos LTI system
Here, we will see how to compute convolution integral. Basically, the convolution integral involves 4 steps as shown below:
Let’s us look at the simple example, x(t) and h(t) is given below:
So follow step 1 to use a dummy variable τ to replace t
then flip h(τ) as indicated in step 2
Repeating step 3 & 4 until obtaining the final answer
so, the final answer is
Similarly, we can also compute the convolution sum for Discrete LTI system by using the following 4 steps:
we will look at some related examples on computing convolution sum in the next post. Stay tuned.