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Matlab/Fast Fourier Transform

  1. Sep 16, 2006 #1
    Hi,
    I am very new to Matlab, and I'm supposed to use the built-in FFT function to do discrete Fourier Transform for f(x) = sin x + 4 cos(5x) + (sin(6x))^2 on the interval [-pi, pi] with a uniform partition for the interval with n = 9. Then I have to
    (a) Plot the magnitudes of the Fourier coefficients and
    (b) Compute the first-order derivates at the grid points via FFT and compare them with f'(x).

    Here's what I have for part (a):

    x = -pi:0.25*pi:pi;
    y = sin(x)+4*cos(5*x) + sin(6*x).*sin(6*x);
    V=fft(y,9);
    plot(abs(V));

    I'm a little confused with what the function fft returns. Does it return the Fourier coefficients of f(x) in my program?

    I got
    V =
    -0.0000
    -5.9965 + 2.1842i
    -4.5019 - 4.8898i
    -8.3033 -15.3964i
    0.8017 + 2.1116i
    0.8017 - 2.1116i
    -8.3033 +15.3964i
    -4.5019 + 4.8898i
    -5.9965 - 2.1842i

    I also don't know how to find the first-order derivates at the grid points via FFT for part (b). What function do I use?

    Thank you very much!

    Regards,
    Rayne
     
  2. jcsd
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