Please take a look at the attached notebook. The first section of the notebook calculates zero for the value of your integral, which is probably not what you intended. The second section shows an example convolution of two functions.
A trick that I use and that may help you is to start with something similar to what I want, but simple enough that it actually gives an answer. Then I make small changes and re-run the calculation to make sure I am still getting an answer. That way I know exactly where I went wrong, and I can go back and try again. For example, if I want to do a calculation with a damped sine, I might start with a square wave, then change to sine, then put in the damping. If my approach doesn't work with the square wave, I look for places to simplify.
I would not use PiecewiseExpand
until I knew the integral was right. Also, I might try integrating just my H[t]
to verify it was not the source of the problem. I would take it apart, until I found something so simple that it worked. Then I would build on that.
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