Understanding Electromagnetic/X-Ray Pulse in Time and Frequency Domain

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Discussion Overview

The discussion revolves around the representation of an electromagnetic/x-ray pulse in both the time and frequency domains, focusing on the implications of pulse shape and line width. Participants explore the characteristics of these representations and their physical meanings.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests that a pulse with fixed energy and finite line width will appear as a vertical line in the time domain when plotting intensity versus time.
  • Another participant clarifies that the line width mentioned refers to the width of the spectrum in the frequency domain, proposing that a delta function represents this case, leading to a constant frequency spectrum.
  • A suggestion is made that a realistic pulse could be modeled as a Gaussian shape, where both the time-domain pulse and frequency spectrum would also be Gaussian, with the relationship that a sharper pulse results in a wider frequency spectrum.
  • One participant questions the physical meaning of a vertical line in the time domain and its corresponding representation in the frequency domain, seeking clarification on the implications of such a representation.
  • Another participant explains that a vertical line in the time domain corresponds to a horizontal line in the frequency domain, indicating that all frequencies are present in an infinitely high and narrow spike.

Areas of Agreement / Disagreement

Participants express differing views on the representation of the pulse in the time and frequency domains, with some agreeing on the implications of a delta function while others explore alternative models like Gaussian pulses. The discussion remains unresolved regarding the best representation and physical interpretation.

Contextual Notes

There are limitations regarding the assumptions made about pulse shapes and the implications of idealized representations, such as delta functions and Gaussian shapes, which may not fully capture realistic scenarios.

Rajini
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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.
 
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Rajini said:
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?
the line width you mention IS the width of the spectrum in the 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.
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
 
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.
 
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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