What Needs to Be Integrated in a Convolution Problem?

[powderchick81]

OK. I understand almost everything I need to know in order to do a convolution problem except how to set up what needs to be integrated. The way my professor does it is:

1) flip the impuse
2) move h(t) over x(t) - we usually do this in 5 different regions
3) for each region the bounds have to be chosen and this I can do but how do I figure out what needs to be integrated?

for this problem you have
0<t<(t-1) and the limits of integration are from 0 to t but what needs to be integrated.

I don't know if I'm getting caught up on the math or what but I do know that I'm completely lost with this. If someone could explain it to me in detail I would greatly appreciate it. I have a test tomorrow and don't want to fail it.

 

[N468989]

Hi, if the amplitude of the impulse is A, and the slope is line equation is y=mx+b (m is the slope, b is 0), you must integrate A*mx from 0 to t. In this case you would get (A*m*t^2)/2

Try the convolution of two impulses, one with amplitude A and another with B.

 

[piercas]

Hi there,

I understand that convolution integrals can be confusing and it's completely normal to have questions about it. Let me try to explain it to you in detail.

First, let's start with the definition of a convolution integral. It is a mathematical operation that combines two functions to create a third function. In simpler terms, it is a way to combine two signals to create a new signal.

Now, let's break down the steps your professor has given you.

1) Flipping the impulse: This is a common step in convolution integrals. It means that you take the function that you want to integrate (usually denoted as h(t)) and flip it horizontally.

2) Moving h(t) over x(t): This step means that you take the flipped h(t) and move it over the function x(t) that you want to convolve it with. This is done in 5 different regions because the two functions may have different shapes and the integration will be different for each region.

3) Choosing the bounds of integration: This step is where you determine the limits of integration for each region. This is usually done by looking at the overlapping area between h(t) and x(t) and choosing the appropriate limits.

Now, for the specific problem you mentioned, the limits of integration are 0 to t and the function is 0<t<(t-1). In this case, what needs to be integrated is the overlapping area between the two functions. To find this, you can graph the two functions and see where they overlap. Then, you can use the limits of integration to determine the area of the overlapping region.

In general, what needs to be integrated in a convolution integral is the product of the two functions. In your problem, it would be the product of 0<t<(t-1) and the flipped h(t).

I hope this explanation helps you understand convolution integrals better. Just remember, practice makes perfect and don't be afraid to ask for help if you're still struggling. Good luck on your test tomorrow!