Fourier Transform

Discussion in 'Homework Help' started by smarch, May 9, 2010.

  1. smarch

    Thread Starter Active Member

    Mar 14, 2009
    52
    0
    [​IMG][​IMG]Hi

    I am trying to find an expression for X(f), when,

    x(t)=exp(-σt)sin(2∏f1t)

    I have attached a screen shot of what I have worked out, but it doesn't seem to be coming together very vell, is there something I am missing in the steps? Or am I right, and how would I integrate that?

    thanks.
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    The Fourier transform of

    u(t)\epsilon^{-\sigma t}sin(\omega_{1}t)

    per table of transforms is

    \frac{\omega_{1}}{\omega_{1}^2+(\sigma+j\omega)^2}

    The u(t) bit tells you the limits of integration are from 0 to plus infinity - otherwise there is no solution if the lower limit goes to minus infinity . The problem can be solved using repeated integration by parts.

    Not sure if this is the same as your problem - given your equation has no reference to the u(t) term - i.e. the Heavyside Function.
     
    Last edited: May 9, 2010
  3. smarch

    Thread Starter Active Member

    Mar 14, 2009
    52
    0
    Hi,

    Thanks for your reply,

    I have attached another JPEG, I have come up with an expression but not sure if it is correct, I did mean to put the limits from 0 to infinity sorry about that.
    However, when i put this into matlab to plot the X(f), i just comes out wrong.
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    This is my method ...
     
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