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Fourier transform of single pulse & sequence of pulses

  1. Nov 22, 2013 #1
    1. The problem statement, all variables and given/known data
    What is the fourier transform of a single short pulse and of a sequence of pulses?

    3. The attempt at a solution
    In class we haven't dealt with the mathematics of a fourier transform, however my professor has simple stated that a fourier transform is simply a equation converter. You can take equations that are a function of frequency and change them to a function of time, and vice versa.

    With that said, i think that the fourier transform of a single short pulse consists of an infinite amount of waves, that destructively interfere everywhere except one place.

    From that i want to say a series of pulses is the sum of many waves that have phase relations that there is periodic constuctive interference, but destructive interference in between. I have no clue if this is correct.
     
  2. jcsd
  3. Nov 22, 2013 #2
    I think you are basically correct
     
  4. Nov 23, 2013 #3

    rude man

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    By 'sequence of pulses' do you mean a finite number of pulses or an infinite number?
     
  5. Nov 23, 2013 #4
    I believe infinite pulses, although the professor didn't specify
     
  6. Nov 23, 2013 #5
    A single very short pulse has (in the limit) an infinate frequency spectrum. This is why one can determine characteristics of a filter by exciting the filter with a single pulse and then doing a fourier transform on the output waveform to determine the filter characteristics.

    A repeated pulse stream has discrete frequencies in the transform. The frequencies are multiples of the frequency of the puilse stream. However, the amplitude of the frequencies are determined by the width of the pulses and will form a Sin(x)/x envelope so to speak.
     
  7. Nov 23, 2013 #6

    rude man

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    What do you mean " .. except in one place"?

    I don't see how you can find the Fourier transform of anything if you haven't dealt with the math.

    If the sequence is infinite in duration (past and future) then the Fourier transform represents an infinte number of discrete frequencies. Those frequencies appear in the Fourier series.
     
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