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Homework Help: Reading frequency spectrum / Fourier Transform and Power Spectra

  1. Nov 25, 2008 #1
    So I have a power spectrum of a given function, which is supposed to be a superposition of four sinusoidal terms with frequencies that range from 1xomega to 4xomega. My spectrum looks something like this:

    What exactly does this spectrum tell me? I know it plots the length squared of a vector that has the real and imaginary components of the amplitude. Mine looks like the top one of the one I posted, its a triangle but mine only has two triangles and the rest are flat lines.

    I unfortunately don't have a book, and the prof only gave us notes on the fourier transform, so I am really stuck here. How do I interpret a flot of these triangles on the frequency-amplitude plot?
  2. jcsd
  3. Nov 25, 2008 #2
    What you have here is the signal (triangular) and its frequency spectrum. There is no superposition of 4 frequencies. Maybe you are mixing it with something else.
    The triangles are the actual signal, with a period of about 4.5 ms (look on the x axis).
    The frequency corresponding to this period is about 220 Hz or 0.22 KHz and this is shown by the first peak in the frequency spectrum. The other peaks are higher harmonics or components (without these you'll have a sin wave with the same period but not a triangular shape).
  4. Nov 26, 2008 #3
    Your questions are a bit unclear.

    If you want to interpret the power spectrum, nasu has already interpreted it for you. I would just like to add on a bit. The frequency spectrum pattern clearly shows a periodic signal in the time domain. This is because of the presence of the impulse function peaks that you see at regular intervals of frequencies (i.e. note that these peaks may not look regular for it is possible to have missing harmonics).

    If the signal in the time domain is NOT periodic, then the spectrum will look continuous, instead of discrete frequency peaks! (Fourier Transform theory)
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