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DSP - Frequency Response of an FIR Filter

  1. Oct 17, 2008 #1
    1. The problem statement, all variables and given/known data
    A linear time-invariant filter is described by the difference equation

    y[n] = x[n] - x[n-2]

    a) Obtain an expresson for the frequency response of this system.

    b) Sketch the frequency response (magnitude and angle) as a function of frequency.

    2. The attempt at a solution

    a) {bk} = {1, 0, -1}
    H(e^-jw)= 1-e^-j2w

    b) I am not sure how to plot the magnitude.

    H(e^-jw)= 1-e^-j2w = (e^-jw)(2*j*sin(w))

    where (e^-jw) is the angle and (2*j*sin(w)) is the magnitude.

    However, there is an imaginary number, j, in the magnitude...what do I do with this?

    Thank you.
  2. jcsd
  3. Oct 17, 2008 #2


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  4. Oct 18, 2008 #3
    OK... so from the notation is seems like cos w is always 0 since the magnitude is


    So would it just be an empty set of axis?
  5. Oct 20, 2008 #4


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    I did a little googling to see if I could find a good reference for plotting complex functions in regards to frequency response. Here's a pdf on FEEDBACK CONTROL that's a bit long but has a good explaination on page 147.

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