# 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