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[mathcad] Phase and Frequency modulation
| [mathcad] Phase and Frequency modulation |
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Author: Lazarus, Max
Posted: Mon, 7 Apr 2008 11:02:32 +0100
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Yes, they do look similar for sinusoids, but digital PSK and FSK are
quite distinct.
Cheers,
Max Lazarus
From: "Paul.Bragg"
"mailto:Paul.Bragg"
Sent: 07 April 2008 10:53
To: "mathcad"
Subject: Re: [mathcad] Modeling White Noise
Hi Tom
Phase and Frequency modulation are, as you say, "almost" the same thing,
but
they are distinct.
Thinking in signal voltages, with zero volts producing zero modulation,
we
have that a steady 1 volt (some positive value) will either, advance the
phase by a fixed amount but the frequency is unchanged (phase
modulation)
or, the actual frequency will rise (change) to a new level equivalent to
an
ever increasing phase for the original frequency (if it was assumed to
have
continued).
Phase modulation is usually done 'fast' so that you can get back to the
nominal quickly, and has special signalling so you can tell which parts
are
the nominal 'phase'. It has only come into its own with modern
electronics.
Old electronics couldn't maintain a reference phase long enough to do
the
comparisons, or do the comparisons fast enough...
and yes, phase is an artificial concept (relative to the reality of a
plain
voltage passing with time), and along with the mathematics that supports
it
is used to confuse lots of folks ;-)
FM does have a lot of noise immunity until it drops below a certain
threshold, where it starts to rapidly fall to pieces. AM doesn't have
that
'rapid threshold' problem so sounds noisy and crackly all the time ;-)
Philip
PS my earlier comment about white noise and thermal noise being the same
is
only true for frequencies below the point that the Plank effect takes
hold
(~THz). Otherwise there would be infinite energy. Plank suggested a
quantum
effect to resolve that problem.
From: Tom Gutman "mailto:Tom_Gutman"
Sent: 06 April 2008 8:44 AM
To: "mathcad"
Subject: Re: [mathcad] Modeling White Noise
Aren't phase and frequency modulation almost the same thing? With
phase modulation by a signal being the same as frequency modulation by
the derivative of the signal? And frequency modulation by a signal
being the same as phase modulation by the integral of the signal? And
aren't differentiation and integration just frequency dependent
scaling, just multiplying or dividing the amplitude of each frequency
component by the frequency? So that phase modulation is just
frequency modulation with a boost to the higher frequencies?
As to the phase/amplitude issue, isn't phase really an artificial
concept? The only real reality being the amplitude at each point in
time? Phase becomes something that is inferred when a signal has
enough structure so that one can identify some sort of repeating unit.
So while the "phase" of white noise has no direct effect, and the
noise does not directly affect the phase, the distortion in the signal
due to the noise reduces the accuracy with which a phase can be
recovered. And such reduction in accuracy occurs long before the
point where frequency and phase become completely unrecognizable.
There is a large measure of immunity to noise using FM, as there is no
directly sensitivity to the noise itself, only to the distortions in
the carrier introduced by the noise, but it is not absolute. AFAIK
the only modulation schemes that have the attributes you propose, a
perfect reproduction up to the point where no reconstruction at all is
possible, are digital rather than analog schemes.
Tom Gutman
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