[time 11] The FT of a single pulse

Stephen P. King (stephenk1@home.com)
Sat, 13 Mar 1999 18:06:20 -0500

Dear Robert,

        I wonder if we could get this guy onboard? :) I found it on DejaNews...


             Re: The FT of a single pulse.
             25 Feb 1999 00:00:00 GMT
             Eric Forgy <ericf@uiuc.edu>
             Center for Computational Electromagnetics

The Heisenberg uncertainty principle is related to this question. In
fact, the uncertainty principle is intimately tied with the Fourier
transform. One of the fundamental properties of Fourier transforms is
that if your pulse is "time-limited", i.e. it goes to zero outside some
window in time, then the spectrum of the pulse cannot be "bandlimited",
i.e. the spectrum extends to infinity.

Translating this to uncertainty, by saying a pulse (wave function) is
timelimited, in effect you are saying that you know with 100% certainty
that the pulse is localized in time. This means that the uncertainty in
frequency (energy) is infinite, i.e. the spectrum (possible energies)
extends to infinity.

The conclusion, pulses localized in time have infinite uncertainty in
energy. Similarly, wave functions localized in space have infinite
uncertainty in momentum.


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