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I FT of a pulse

  1. Sep 5, 2016 #1
    Dear All,
    Suppose we have a electromagnetic/x-ray pulse with fixed energy with finite line width. I want to know the schematic of a plot how it looks in time- and frequency-domain?
    I think I understand in time domain: there will a straight vertical line on plotting intensity vs time in x-axis.
    Regards, raj.
     
  2. jcsd
  3. Sep 5, 2016 #2

    BvU

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    the line width you mention IS the width of the spectrum in the frequency domain.
    In that case you have a delta function; the frequency spectrum for that is a constant for all frequencies.

    You have to compromise for realistic cases; the easiest is a pulse with a gaussian shape: the frequency spectrum is also a gaussian. The sharper the pulse, the wider the frequency spectrum.
    Check out some fourier transforms
     
  4. Sep 6, 2016 #3
    Hello,
    So if there is a vertical line in the time domain then it will be a horizontal line in the frequency domain. If yes, please give me the physical meaning!
    Thanks, raj.
     
  5. Sep 6, 2016 #4

    BvU

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    The physical meaning is that all frequencies are present in an infinitely high and infinitely narrow spike ...

    If that isn't very satisfactory: check out the link I gave you:
    • The ##\delta(t)## is second from last on page 1.
    • You can see it as a limiting case of a rectangular pulse (#4 on page 2) with ##\tau\downarrow 0##
    • Or as a limiting case of a gaussian pulse (#3 on page 3) with ##\sigma\downarrow 0##
    • etc
     
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