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Fourier Properties (shifting)

  1. Oct 21, 2014 #1
    Hi, I need help with some basic fourier transform properties stuff - its fairly simple though I think I am doing something wrong.

    So we know from the shifting property
    if h(x) has the fourier transform H(f)
    then h(x-a) has the fourier transform H(f)ei*2*π*f*a

    so I have the function

    cos(2πf0x - π/4)

    I know (from a previous question) that the fourier transform of cos(2πf0x) is

    ½[δ(f+f0) + δ(f-f0)]

    where δ indicates the delta function.

    so then if we factor above

    cos(2πf0x - π/4)
    cos(2πf0(x - 1/(8f0)))

    so then shouldn't the answer be that the fourier transform is

    {½[δ(f+f0) + δ(f-f0)]} * exp(i*pi*f/(4f0)

    I don't see if I did anything wrong here - and further, can this be simplified more?

    Thanks
     
  2. jcsd
  3. Oct 26, 2014 #2
    Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Oct 27, 2014 #3

    mathman

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    Science Advisor
    Gold Member

    part of statement starting at "so if we factor the above" is very unclear.
     
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