I FT of a pulse

1. Sep 5, 2016

Rajini

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. Sep 5, 2016

BvU

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

3. Sep 6, 2016

Rajini

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.

4. Sep 6, 2016

BvU

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