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Finding the filtered output signal

  1. Mar 12, 2008 #1
    A causal LTI filter has the frequency response H(jw) shown in the graph. For each of these input signals, determine the filtered output signal y(t).

    1) x(t)=exp(jt)

    2) x(t)=(sin(wt))u(t)

    3) X(jw)= 1 / ((jw)(6+jw))

    4) X(jw)= 1 / (2+jw)

    I don't understand what I have to do to find y(t), any help is appreciated, thanks
     

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  3. Mar 12, 2008 #2

    rbj

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    what is the function description of [itex]H(j \omega)[/itex]? can you extract that out of the graph?
     
  4. Mar 13, 2008 #3
    nothing much in the graph, just a straight line from (-1, 2j) to (1, -2j)
     
  5. Mar 13, 2008 #4
    There are many ways to find y(t):
    y(t) = h(t) * x(t) convolution
    y(t) = F(H(jw)X(jw)) fourier transform of Y(jw)
    y(t) = H(jw)x(t) amplitude scaling if x is an eigenfunction

    Which one is most applicable? Or which have you learned?
     
  6. Mar 15, 2008 #5
    yes, i learned it before, so is it correct to say H(jw)= -w?
     
  7. Mar 15, 2008 #6
    y"t" = h(t) * x(t)
    y"t" = f(H(jw)X(jw)
    y"t" = h(jw)x(t)
     
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