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Need this derivation to solidify understanding

  1. Apr 1, 2009 #1
    Can someone please give a concise and complete derivation of the following Fourier Transform:

    x(t) = e^(j*w0*t) (w0 is a constant)

    Please explain all parts. Thank you very much!
     
  2. jcsd
  3. Apr 1, 2009 #2
    Consider the relation

    z(t) = A[cos(w0t) + i sin(w0t)] in the complex plane

    Where z(t) is a complex variable z(t) = x(t) + i y(t)

    For the differential equation d2x/dt2 + w02 x = 0
    the solution is x = A ei w0 t

    where ei w0 t as a rotating unit-amplitude vector in the complex plane and i = sqrt(-1):

    z(t) = A ei w0 t
     
    Last edited: Apr 1, 2009
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