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Real Sequence As Rational Function in e^-jw

  1. Feb 15, 2005 #1

    dduardo

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    Staff Emeritus

    How do I convert a piece wise function like this:

    y[n]=

    {1 -N<=n<=N
    {0 otherwise

    to something like this:

    p0+p1e^(-jw)+...+pMe^(-jwM)
    ------------------------------
    d0+d1e^(-jw)+...+dNe^(-jwN)

    Basically, what formula do I need to use to calculate the coeffients?

    [Edit] I'm trying to use the matlab function FREQZ, but requires the formula to be in the above format.
     
    Last edited: Feb 15, 2005
  2. jcsd
  3. Feb 15, 2005 #2

    learningphysics

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    Homework Helper

    Well, that looks the frequency response of a discrete time system.

    I might be wrong, but I'd first get the z-transform of your sequence:

    z^N + z^(N-1) + z^(N-2) + .....+ 1 + z^(-1) + z^(-2) + ....z^(-(N-1))+z^(-N)

    then plug in z=e^(jwdt)

    dt is the time between samples.

    e^(jwdtN) + e^(jwdt(N-1)) + .....+ 1 + e^(-jwdt) + e(-jwdt2) + .... e^(-jwdtN)

    So that would be your numerator, and the denominator is just 1. Is that form acceptable?
     
    Last edited: Feb 15, 2005
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