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.