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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

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    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
     
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