Find Fourier Transform of sampled signal by application of Convolution Theorem

Discussion in 'Homework Help' started by VVS, Jan 8, 2009.

  1. VVS

    Thread Starter Active Member

    Jul 22, 2007
    66
    0
    Hello,

    I saw some derivations for the the Fourier Transform of a sampled signal in books such as BP Lathi, but I was just wondering whether there is another way and i thought of this way:

    basically the sampled signal in time domain is just the signal in time domain multiplied by the sum of delta functions in time domain.
    So if we take the Fourier Transform of the whole equation we could apply the Convolution Theorem, (A multiplication in the time domain corresponds to a Convolution in the frequency domain).

    I did this and I do get a result but quite a weird one.

    I uploaded my working (page 1 is bild.jpg and page 2 is Bild001.jpg).
    I would be very thankful if someone could point out what i got wrong.
    thx
    VVS
     
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