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Fourier Transform deduce the following transform pair

  1. Nov 4, 2015 #1

    grandpa2390

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    Gold Member

    1. The problem statement, all variables and given/known data
    I'm supposed to be using the similarity theorem and the shift theorem to solve:

    cos(πx) / π(x-.5) has transform e^(-iπs)*Π(s)

    2. Relevant equations
    similarity theorem f(ax) has transform (1/a)F(s/a)
    shift theorem f(x-a) has transform e^(-i2πas)F(s)

    3. The attempt at a solution
    I don't know. cos(πx) has the impulse pair transform and the impulse pair function has cos(πs) transform.
    the only term that I can get is that the shift theorem will give me a e^(-iπs) because the 1/2 in the impulse function. I don't understand how to get the rect(s) term in the transform.
     
  2. jcsd
  3. Nov 4, 2015 #2

    blue_leaf77

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    Science Advisor
    Homework Helper

    Use the fact that ##\sin(\pi x - \frac{\pi}{2}) = -\cos(\pi x)##.
     
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