# Trouble with convolution and system response to inputs

1. Sep 18, 2011

### Lolsauce

1. The problem statement, all variables and given/known data

x(t) is input, h(t) is the impulse response, y(t) is output

Find the system response to the input x(t)

x(t): [PLAIN]http://img10.imageshack.us/img10/5157/55570988.jpg [Broken]

h(t): [PLAIN]http://img593.imageshack.us/img593/1079/52492104.jpg [Broken]

2. Relevant equations

Now I know the convolution integral is (f*g)(t) = [URL]http://upload.wikimedia.org/math/d/1/2/d122f80c065a111d4617fb3afdae0e53.png[/URL]

But for this problem I took a more graphical approach

3. The attempt at a solution

I changed the variable to T (Tau) and chose a function to be time reversed

So I took the input and shifted then reversed the graph giving me this:
[PLAIN]http://img13.imageshack.us/img13/8581/xtshiftandreverse.jpg [Broken]

Afterwards I found t in which the graphs starts overlapping and not overlapping. I found at for t < -1, convolution c(t) = 0. So for my first intervals I looked at -1 < t < 0, which overlapping begins.

[PLAIN]http://img703.imageshack.us/img703/5655/widthj.jpg [Broken]

This gives me a width of (t-2) - (-3) = t + 1 which should be the equation from -1<t<0.

I repeat the same process from 0 < t < 5, and this give me an obviously overlap and convolution of c(t) = 1.

Then for the overlap starts to leave, I get and equation of:
(t-3) - 3 = t - 6, this is from the endpoint of x(t-T) leaving h(t).

So at the end I get this graph, it seems kind of whack. Especially the first interval of -1 < t < 0. Can anyone give me some tips or see a mistake I've done.

[PLAIN]http://img69.imageshack.us/img69/7213/convolution.jpg [Broken]

Last edited by a moderator: May 5, 2017
2. Sep 18, 2011

### Lolsauce

Nevermind, I just solved it, lolsauce. I turns from -1 < t < 0 the equation is t + 1, means it is shift to the right by one, NOT shifted up like I had thought.