Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
Subject: Re: How does a mixer work?
X-Newsreader: Microsoft Outlook Express 6.00.2800.1106
Date: Sun, 27 Oct 2002 08:29:04 -0000
NNTP-Posting-Date: Sun, 27 Oct 2002 08:29:07 GMT
"Norman Yarvin" wrote in message
> In article <3DB947CA.DCFA6601@webaccess.net>,
> Chuck Simmons wrote:
> >Kevin Aylward wrote:
> >> This is expressed by Sigma_F * Sigma_T >=1/2. The standard
> >> are determined by the shape of the pulse and the shape of the
> >> Fourier transform. Noise is not involved at all.
> >The difficulty here is that standard deviation is pretty meaningless
> >the absence of noise. In fact, it is zero identically.
No, "rms voltage" is identical to "standard deviation of the voltage".
rms has lots of uses independent of noise.
> No, the meaning is: pretend that function F and the function T were
> probability distributions, and take their standard deviations. (As
> 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).
Ahmmm.. Why won't people listen.
Look, I said it has nothing to do with noise and I meant it. This is
*not* debatable. Its in any decent book in communication theory. I did
not invent any of this.
The source of your confusion is that you have forgotten that the
"standard deviation" also has another equally valid name, i.e. "root
mean square". rms does not imply noise.
For the last time:
Consider a *deterministic* pulse, in the *absence* of noise. It has some
*definite*, but *arbitrary* extent form 0 to infinite time. It might be
gaussian, or triangle or any shape whatsoever. Because it aint
necessarily a rectangle, it width needs to be defined. So, calculate its
rms width. Take the Fourier transform of the pulse. Calculate the rms
width of its frequency spread. We have.
no matter what the pulse shape is.
> 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.
Maybe, but I am not introducing statistics at all. The pulse and its
Fourier transform are deterministically specified.
As I noted, the HUP, is an immediate deduction of the above pure
mathematical result above, once you *physically* associate space and
momentum as Fourier transforms of one another. Without the above
mathematical result, the HUP would not exist.
> This isn't electronics design,
Yes it is, its called signal analysis. However, its probably a bit
advanced for those with just an electronics background, i.e. circuits
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.