FFT and Fourier Series

Discussion in 'Physics & Math' started by Heitor, Sep 2, 2002.

  1. Heitor Registered Member

    Messages:
    1
    Hello.

    Consider function f(t) of period T and frequency omega=2*pi/T.
    It's representation by a truncated Fourier series is:

    x(t)=0.5*A0+sum(n from 1 to N) (An*cos(n*omega*t))+sum(n from 1 to N) (Bn*cos(n*omega*t))

    A0=2/T*integral(from 0 to T) f(t) dt
    An=2/T*integral(from 0 to T) f(t)*cos(n*omega*t) dt
    Bn=2/T*integral(from 0 to T) f(t)*sin(n*omega*t) dt

    I can find the A and B coefficients by direct integration but I think that I can use the fft function in matlab to do it faster. Supose we store the fft of the sampled f(t) in the vector F.
    But how to identify the A and B in the fft result?
    The A0 coefficient is the real part of the first element of F. The A1 is the real part of F(2), the B1 is the imaginary part of F(3) and so on. Is this right?
    And how about the frequency? The frequency corresponding to F(2) is not omega... And the frequency corresponding to F(3) is not 2*omega. Am I right? Or not? Why?
    Please, help meeeee!!!

    Thank you,
    Heitor
     

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