I'm learning about the convolution sum and convolution integral, but I would like to know the importance of convolution sum/convolution integral in signals and systems. I know it sounds kind of silly, but I feel like if I learn the importance of convolution, I can learn it better.

 

Take a look at this wikipedia presentation complete with a crude animation.

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I'm learning about the convolution sum and convolution integral, but I would like to know the importance of convolution sum/convolution integral in signals and systems. I know it sounds kind of silly, but I feel like if I learn the importance of convolution, I can learn it better.

The convolution sum and convolution integral are the foundation which LTI system theory is built on. The convolution operation is the tool that allows you to calculate the output time dependent response of an LTI system for any input signal. Aside from being this practical tool, the conceptual understanding of convolution is critical for all further study in this area. Eventually you learn that multiplication of transfer functions and transformed signals in the frequency domain is equivalent to convolution on the time domain. And, then you go on from there.

It's not silly at all to try to know the applications as a way to make learning easier, but it's also important to understand that learning the tools and comprehending the importance in applications go hand in hand to some extent. So, when someone else tells you the application, it's not as impressive as when you actually use it youself in an application.

 

You literally implement a discrete convolution sum as FIR filters all the time

 

Entire signals and systems and communication depends and revolves around convolution. There are several places where it is crucial(take a look at the wikipedia applications page but that's not all there are several other places where you can use it). So learn it well and understand. Without it it is impossible to study communication. Do feel free to ask any questions related to it.

 

You'll learn about FIR filters later in your courses. It is one of two major types of digital filters you can perform and it is the easiest to program. Think about removing analog filters in your design and replacing them with configurable filters via software.

When you design an FIR filter, you will get a list of coefficients. When you convolve these coefficients with an input signal you get out a filtered signal.