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Calculating inverse DTFT

  1. Mar 1, 2017 #1
    1. The problem statement, all variables and given/known data
    There is a signal y[n] with a differentiable DTFT Y(eiw). Find the inverse DTFT of i(d/dw)Y(eiw) in terms of y[n] (where of course i = √-1).

    2. Relevant equations
    Sifting property ∫eiwndw = 2π*δ[n] from [-π,π] (integral a) leads to ∫Y(eiwn)dw = 2π*y[n] from [-π,π] (integral b) which I derived in a previous question.

    3. The attempt at a solution
    Not sure where to start as I don't actually understand what i(d/dw) is. Is it a transposition of some sort? How do I include i(d/dw) into integral b above? It isn't true that n = 1 in this case...is it? Am I perceiving this to be more complicated than it is?
  2. jcsd
  3. Mar 4, 2017 #2
    i(d/dw) is simply an operator: it means differentiate w.r.t. w and multiply the result by i.
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