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Fourier Transform

  1. Apr 8, 2007 #1
    I am stumped on this...

    Given a discrete function, and transform pair: [tex] x(n) \leftrightarrow \hat x (e^{j\omega}) [/tex]

    What is the transform of:
    [tex] x_3(n) = (n-1)^2 x(n) [/tex]

    I really don't know how to do this. I have a table proprety for [itex] nx(n) [/tex], but nothing with [itex] n^2 x(n) [/itex]. The only thing I can think of is expanding it as: [itex] x_3(n) = (n-1)^2x(n) = n^2x(n) - 2nx(n) +x(n) [/itex]... but I'm stuck on the [itex] n^2 [/itex] part. My intuition says that it has something to do with the differentiation property, but I'm really stuck, and can't figure this out. Any help would be awesome. thanks :)
  2. jcsd
  3. Apr 9, 2007 #2
    Easy. Got it finally.

    Just write [tex] x_3(n) = ny(n) [/tex]
    where [tex] y(n) = nx(n) [/tex]

    and since I have the transform for [itex] nx(n) [/itex], it is cake.
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