1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Convolution of periodic signals

  1. Dec 2, 2012 #1
    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. jcsd
  3. Dec 3, 2012 #2
    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.
  4. Dec 3, 2012 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook