Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
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Subject: Re: How does a mixer work?
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Date: Tue, 22 Oct 2002 07:47:36 +0100
NNTP-Posting-Date: Tue, 22 Oct 2002 07:47:41 BST
"Chuck Simmons" wrote in message
> Kevin Aylward wrote:
> > I have just explained, it don't matter how accurate the time
> > is. Its that simple. It a basic physics of the Fourier
> > pair.
> There is no physics involved at all.
Oh. I see.
The Fourier transform is a
> mathematical construct and is not physics at all by any means and
> can be.
The Fourier transform is used to model physical processes. If the model
is correct, so are the physical results the mathematical model predicts.
>It is quite impossible to argue a mathematical point using
> physics as the basis.
>It is entirely wrong and cannot be justified.
Of course it can.
The point I am making is a real physical point, a proof based on the
mathematics. Lets assume that it is valid to model a physical signal in
both the time domain and frequency domain. If this assumption is
invalid, then we might as well go home as we cant form a discussion at
all. So we set up a one to one correspondence with reality and the
mathematics. We now do some sums in the math domain, we can then use
that one to one correspondence to "prove" results back in the real
Consider a *real* pulse with a funny wave shape. Take the standard
deviation of that pulse. Now do a Fourier transform of that pulse, it
will also have a funny shape, indicating a spectrum of frequencies. You
can check the math by using a spectrum analyser on the pulse. So we have
two numbers Dt, Df. It can be shown mathematically that:
This means that, in the *real* universe, if you want a narrow frequency
spectrum, i.e. you know what the frequency is within a narrow range of
value Df, the time shape of the pulse must be large. That is, you will
have to measure over a long period to get an accurate measurement of
frequency. This is fundamental. No way around it.
The issue here is that you simple assert that you can measure a
frequency with an arbitrary accuracy, but the detailed mathematical
model of the situation, shows that this cannot be done. Measuring a
frequency, requires a measurement time. If the time is short, there
*must* be a resulting error in the measurement. So, in the case where
you switch on and off a signal, you cant measure the carrier for longer
then the pulse on time. This inherently limits the accuracy of the
The root of this is that a fixed frequency can only be true, if the sine
wave has been on since the dawn of time.
> There are some charlatan mathematicians who do it but they are never
> taken seriously. Certainly, in my educational career, I heard such
> incredible nonsense from physics professors that I can't take you
> seriously if you use physics as authority in mathematics.
Your arguing from ignorance. However, I agree there are some
mathematicians that overstep their boundary.
> > Look, its clear you don't really have a sufficient background of
> > analysis to be discussing this.. Nor, man enough to admit it.
> You haven't a clue what my background is and really can't comment
> it without knowing. If you are astute, you may have noticed I have
> in and around electronics for 40 years or more and most of that as an
> engineer. However, I don't have an engineering educational background
And this is obvious. I understand that you have a raesonable knowledge
in elcetronics, however, this lack of a formal background is indeed
obvious. You would do yourself a favour to respect when a more
knowledgeable view is being put forward.
I avoided that for a number of reasons not the least of which is
> that I never wanted to be an engineer.
I didn't/don't either.
>If I hadn't run out of money in
> 1980, I wouldn't be an engineer but that is ancient history. I have,
> various times, studied harmonic analysis in particular. However, as
> physics plays no role in harmonic analysis, I am not familiar with any
> of your physics arguments
I know you dont.
(which, of course, have nothing whatever to do
> with harmonic analysis).
But they do with regards to a real, physical system.
> Anyway, you seem to be on the numerical side of things. I detest
> numerical analysis and do it under duress.
I have shown you an inescapable problem in measuring properties in the
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.