Convolution of periodic signals

[scubaman]

Homework Statement

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)

Homework Equations

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

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.

 

[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.

 

[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