# Convolution of periodic signals

1. Dec 2, 2012

### scubaman

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

Consider an LTI system with impulse response h(t) = (0.5sin(2t)/(t)

Find system output y(t) if x(t) = cos(t) + sin(3t)

2. Relevant equations

y(t) = x(t)*h(t)

3. The attempt at a solution

I am only familiar with doing much simpler convolutions using graphical analysis and thus do not know how to begin one like this.

2. Dec 3, 2012

### aralbrec

Do you have to do this in the time domain? You must have covered that time domain convolution is equivalent to multiplication of spectrums in the frequency domain?

Your h(t) = sin(2t)/(2t) = sinc(2t) is a rectangle in the frequency domain so it would be very easy to find the response to two sinusoids in the frequency domain.

3. Dec 3, 2012

### rude man

Use the convolution integral:

y(t) = x(t)*h(t) where
x(t)*h(t) = ∫h(τ)x(t-τ)dτ with integration limits of 0 and t.

* denotes convolution