Continuous time Convolution?

Thread Starter

skyline977

Joined Jan 14, 2021
29
Hi all,

I am trying to do convolution for the function below
njKeI.png

The correct solution is as follows:

W3Ubx.png

I tried solving the problem, below is my attempt:
eoqi8.jpg
gJ9XF.jpg


Can you please advise me where I went wrong?
 

MrAl

Joined Jun 17, 2014
8,479
Hi all,

I am trying to do convolution for the function below
View attachment 227998

The correct solution is as follows:

View attachment 227999

I tried solving the problem, below is my attempt:
View attachment 228000
View attachment 228001


Can you please advise me where I went wrong?
Hello,

This is interesting because it looks like your intervals with "8-2*t" and before that are correct. A sanity check tells us that it would make sense that the output decreases when x(t) decreases, and with the solution they give for t>2 it does not but yours does.
However, i would expect the output waveform to be continuous such that there should be no jumps when we go from one interval to the next, and that is because each interval start time is the same time as the previous interval end time. For example, with 8-2*t for t=3 we get 8-6=2 but the next interval you have 4*(4-t) and with t=3 we get 4. So we get two different y values at the same time instant so that 4*(4-t) must be wrong.

It also looks like your intervals 5 and 6 are correct.
 
Last edited:

Thread Starter

skyline977

Joined Jan 14, 2021
29
Hello,

This is interesting because it looks like your intervals with "8-2*t" and before that are correct. A sanity check tells us that it would make sense that the output decreases when x(t) decreases, and with the solution they give for t>2 it does not but yours does.
However, i would expect the output waveform to be continuous such that there should be no jumps when we go from one interval to the next, and that is because each interval start time is the same time as the previous interval end time. For example, with 8-2*t for t=3 we get 8-6=2 but the next interval you have 4*(4-t) and with t=3 we get 4. So we get two different y values at the same time instant so that 4*(4-t) must be wrong.

It also looks like your intervals 5 and 6 are correct.
Thank you,
You are right and I fixed it and it matches as follows:
IMG-1978.jpg
 
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