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Fourier Transform Analysis

  1. Jun 6, 2006 #1
    Unfortunately I haven't really been able to find anything to help me on how to interpret fourier transforms and I need some help.

    This is the question I am trying to do.

    The superposition of two signals of the same amplitude but different frequencies and phase is responsible for the acoustic phenomenon of beats. If the two signals y1(t) and y2(t) are given by the expressions below:

    y1(t)=[tex]Acos(\omega_1[/tex]t-[tex]\phi_1)[/tex]

    and

    y2(t)=[tex]Acos(\omega_2[/tex]t-[tex]\phi_2)[/tex]

    Then the expression for the superposition is:

    y = [tex]Acos(\frac{1} {2}(\omega_1-\omega_2)t+\frac{1} {2}(\phi_1-\phi_2))[/tex][tex]cos(\frac{1} {2}(\omega_1+\omega_2)t+\frac{1} {2}(\phi_1-\phi_2))[/tex]

    The file exam05final.txt contains 512 samples of just such a superposition sampled at 5.12 Hz. Your task is to determine as much as you can about the two signals, and if possible confirm your deductions


    The first link below is the screenshot of the plot of the plain superposition signal. The second link below is the screenshot of the FFT output plot that I managed to get.
    I guess the two peaks show the two frequencies that are within the superposition signal.

    Link 1 = [​IMG]
    Link 2 = [​IMG]

    A hint for obtaining more information on the two signals is to "recreate the time series by taking out phase difference and double amplitude
    in bin 50 and sample=5.12Hz .:. each bin=.01Hz .:. each omega=.21 pi"

    I don't have any idea of how to do this at all and would appreciate the slightest bit of help.

    Thanks
     
    Last edited: Jun 6, 2006
  2. jcsd
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