From: Norman Yarvin
Subject: Re: How does a mixer work?
NNTP-Posting-Date: Sat, 26 Oct 2002 20:33:11 EDT
Date: Sun, 27 Oct 2002 00:33:11 GMT
In article <3DB947CA.DCFA6601@webaccess.net>,
Chuck Simmons wrote:
>Kevin Aylward wrote:
>> This is expressed by Sigma_F * Sigma_T >=1/2. The standard deviations
>> are determined by the shape of the pulse and the shape of the pulses
>> Fourier transform. Noise is not involved at all.
>The difficulty here is that standard deviation is pretty meaningless in
>the absence of noise. In fact, it is zero identically.
No, the meaning is: pretend that function F and the function T were
probability distributions, and take their standard deviations. (As in,
the expected value of F is integral x*F(x) dx, etcetera.)
Then there is some inequality of the sort Kevin says (though I can't
vouch for its exact form).
The reason why anyone would pretend that F and T were probability
distributions, and call the above formula the Heisenberg uncertainty
principle, is that they had quantum physics in mind. In quantum physics,
the behavior of a particle is entirely governed by a wavefunction: the
position and velocity of the particle is random, with the probability
distribution of its position being the wavefunction, and the probability
distribution of its velocity being the Fourier transform of the
wavefunction. So quantum physics involves situations where the two
functions (the function and its Fourier transform) really are probability
distributions. (Actually I think one has to take the absolute values of
those functions, to get the probability distributions, but that's the
This isn't electronics design, but it isn't complete bullshit either.