Using an FM-Carrier for the Y [Luminance] Signal -- how to relieve the bandwidth issue?

On Sat, 27 Oct 2007 01:45:25 -0700, "Green Xenon [Radium]"
wrote:

Dave Platt wrote:

In article ,
Green Xenon [Radium] wrote:


So there is no way to decrease how far the sidebands will go?


With FM? Nope, not in the way you're hoping. Modulate a carrier Fc
with a frequency Fm, and the first sidebands will be at Fc+Fm and
Fc-Fm, just as would be true with AM. That's the narrowest you can
get.



So a higher-frequency modulation signal will result in more distant
sidebands than a lower-frequency modulation signal? E.g. a 10,000 Hz
tone will result in sidebands further from the base carrier frequency
than a 1,000 Hz signal?

No, this is not true.

Both the 10,000 Hz and the 1,000 Hz tones will produce sidebands which
extend to infinity.

In article , George
wrote:
On Sat, 27 Oct 2007 01:45:25 -0700, "Green Xenon [Radium]"
wrote:


So a higher-frequency modulation signal will result in more distant
sidebands than a lower-frequency modulation signal? E.g. a 10,000 Hz
tone will result in sidebands further from the base carrier frequency
than a 1,000 Hz signal?

No, this is not true.


...although it will be the case with the 10kHz modulation that none
of the sidebands will be closer than 10kHz from the carrier. Whereas
with 1kHz modulation they will start at 1kHz.

Both the 10,000 Hz and the 1,000 Hz tones will produce sidebands which
extend to infinity.

That is what textbooks say about an ideal case of one sinusoid modulated
with another.

But I suspect the posting you responded to assumed that we were talking
about sideband components with power levels significant enough to matter in
relevant real-world situations. Possibly even assuming the same sort of
peak deviation level without saying so. ;-

Fortunately:

A) The amplitude of the sideband components tends to fall rapidly towards
infinitesimally small as you move very far away from the carrier. Bessel
functions of the relevant type are like that.

B) Real world situations generally don't use ideal sinusoids, nor require
zero distortion. Nor use modulators and demodulators with infinite
bandwidths. Thus real modulation bandwiths have a tendency to be finite.

Thus reality only approximates to the simple textbook analysis you base
your statement upon. (Most texts avoid more complex modulations and the
effect of finite TX bandwidths like the plague as they can be a nightmare
to model analytically or explain, certainly at an undergrad level! The
tendency is to do simple mod, quote Carson's Rule, and quit while you
are ahead. :-) )

So - unless your interest is purely in trying to score a debating point by
nit-picking based simplifying what appears in undergrad texts - what was
your point? :-)

Slainte,

Jim

--
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Audio Misc http://www.audiomisc.co.uk/index.html
Armstrong Audio http://www.audiomisc.co.uk/Armstrong/armstrong.html

On Sat, 27 Oct 2007 17:56:13 +0100, Jim Lesurf
wrote:

So - unless your interest is purely in trying to score a debating point by
nit-picking based simplifying what appears in undergrad texts - what was
your point? :-)

Slainte,

Jim

If you examine this thread you might conclude that the question was
asked by someone seeking knowledge.

The first respondant took advantage of this to provide a sarcastic
put-down, which, incidentally, exposed his own ignorance.

Can you imagine the feelings of the questioner upon reading that
response to his honest question ?

That response was typical of many postings in this flaming Newgroup.
Your own posting is made entirely in the same spirit and you should be
ashamed.

By George.

In article , George
wrote:
On Sat, 27 Oct 2007 17:56:13 +0100, Jim Lesurf
wrote:

So - unless your interest is purely in trying to score a debating point
by nit-picking based simplifying what appears in undergrad texts - what
was your point? :-)

Slainte,

Jim

If you examine this thread you might conclude that the question was
asked by someone seeking knowledge.

If you examine the thread *in uk.tech.digital.tv* where I am reading and
replying, you will see that the start of the discussion was missing as only
some responses have been posted here. Afraid my conclusions are only
based on what has been posted where I read it.

The first respondant took advantage of this to provide a sarcastic
put-down, which, incidentally, exposed his own ignorance.


Can you imagine the feelings of the questioner upon reading that
response to his honest question ?

It might help if you addressed what I wrote about *your* posting. :-)

I was 'imagining' the feelings of the person whose posting I saw
you dismiss as untrue when you said that, but didn't give an
explanation which would have helped him to understand that, or
your comment.


That response was typical of many postings in this flaming Newgroup.


Not clear which "flaming Newsgroup" you mean here.

Your own posting is made entirely in the same spirit and you should be
ashamed.

As things stand I am unable to comment. I am sorry if you are upset,
but perhaps you should have explained more clearly when you dismissed
what someone else as not being "true". That way the "spirit" of your
contribution would have been seen by me as being helpful rather than
- as here - critical. :-)


Slainte,

Jim

--
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Audio Misc http://www.audiomisc.co.uk/index.html
Armstrong Audio http://www.audiomisc.co.uk/Armstrong/armstrong.html

In article , Green Xenon
[Radium] wrote:


Sorry but I am now confused. Dave said that a higher-frequency modulator
signal will result in wider sidebands than a lower-frequency modulator
signal. George says no to that. Jim then goes on about how it may or may
not be true. I am getting really confused.

Will someone please assist me in clearing this up?

The problem here is that what 'George' said may well have confused your
understanding by introducting a point which is textbook correct, but was
misleading for you in this context without other information. That is why I
responded to him as I did, as I have see similar problems on many occasions
when undergrads have been confused in similar ways. Teaching requires
judgement about how you explain things, as well as patient effort by the
learner. :-)

To actually understand it is generally useful to start with a simplified
description and then only add in details later in a way that builds on the
initial, established, understanding. The snag is that this allows people to
nit-pick and point-score to show off how clever they are, but risks
confusing the person who wanted to learn, or make them think it is all to
complex for them to follow.

There is a fuller explanation of this in textbooks, and on the 'Scots
Guide' (address in my sig, below). But that is aimed at the undergrad level
student and assumes you're happy with the maths, so here is something
simpler.

Consider an example. Take a 1MHz sinusoid and modulate its frequency.

This 1MHz signal is often called the 'carrier' and we'd then say we have a
'carrier frequency' in this case of 1MHz.

Consider applying modulation with a 1kHz sinusoid as the modulation
waveform.

When considered as a sprectrum the result can be described as a series of
'sideband' components, spaced 1 kHz apart, centered on the carrier
frequency. So we'd get components at 1MHz + 1kHz, 1MHz + 2kHz, 1MHz +
3kHz, etc. Also at 1MHz - 1kHz, 1MHz - 2 kHz, etc...
In general, there will also still be a component at 1MHz.

The general rule is that the components are spaced at intervals equal to
the modulation frequency.

So if we'd used 10kHz modulation instead, then the sideband components
closest to the carrier would have been at 1MHz +/- 10kHz, the others at
+/-20, +/- 30, etc... Thus the interval between them has changed.

From the maths in the textbooks, these components nominally extend over an
infinite frequency range. But in reality they don't, and they amplitudes
tend to fall away to being insignificant when you look at frequencies a
long long way from the carrier.

The distribution of the amplitudes or powers of the components depends on
how large the modulation is, as well as the modulation frequency. So, all
else being equal, if you apply, say, 10kHz modulation, the components with
significant power levels will tend to spread out over a wider range of
frequencies than if we'd used 1kHz modulation.

The precise meaning of "significant power levels" will depend on the use
the FM system is being put to, and the conditions in which it is used.
However a general rule-of-thumb people use is 'Carson's Rule'. (If
interested in that, look for it on the Scots Guide.)

Thus the point you made in your first posting in this thread *as it has
appeared in the uk.tech.digital-tv group* is close to being correct, but
there are problems with your wording which would need clarifying.

All else being kept the same, Increasing the modulation frequency tends to
spread out the sideband power distribution and thus requires a wider
bandwidth. In practice a wider bandwidth tends to be required.

But purely in terms of undergrad textbooks, any sinusoidal modulation of a
sinusoid tends to give 'components' over an *infinite* range, so on that
basis what 'George' said is formally correct, and your wording wrong. Since
the components theoretically extend over an 'infinite' range, you can't say
that increasing the modulation frequency will "result in sidebands further
from the carrier" without qualifying that in some way like allowing for the
power levels, or some equivalent. What happens that the distribution of
power tends to spread out over a wider range of frequencies. (And hence the
information also tends to do so.)

The points he omitted are that some of [1] these 'components' well away
from the carrier may be of a size close enough to zero to be of no real
relevance, and that in real world systems no modulator or demodulator can
produce 'infinite' bandwidths. Thus he was showing he'd read the textbooks
which you hadn't, but confused you in the process. He was introducing the
formal need in the maths for an infinite set of components, where many/most
[1 again] of them will be infinitestimally small in power.

It would have been better if he'd then explained this, rather than simply
pronouncing that your comment wasn't "true". That way, his posting would
have been more helpful, rather than confusing for you. But it is always
easier - and quicker - to say someone else is wrong than it is to try to
give a useful explanation yourself. Explanations like this take time,
and may simply prompt someone else to nit-pick. :-)

If you want an example of how the modulation frequency affects the
spectrum, have a look at

http://www.st-and.demon.co.uk/temp/fmspectra.html

note, though, that this page was produced for another purpose so
uses more complicated modulations than a simple sinusoid. In
this case to show the effect of stereo (difference) modulation on
traditional stereo FM broadcasts. In this example the L-R or Right
only signals end up being modulation with higher modulation
frequencies, so tend to spread out the power-frequency spectrum
of the result. The first graphic shows this most clearly.


I'm afraid I can't comment on what might have been said in this discussion
prior to it starting being cross-posted to uk.tech.digital-tv as I haven't
seen that. If you or anyone else is simply engaged in a wind-up or trolling
I haven't seen that. So if what I write does not fit that context I am not
in a position at present to take that into account. Similarly, if 'George'
has lost patience as a result of fol-de-rols before this thread popped
up here in uk.tech.digital-tv I have no awareness of that, so can't
respond on that.

Slainte,

Jim

[1] Indeed infinitely many of them will be of infinitestimally small
amplitude. 8-] You could even have wonderful nit-picking debates about
if this was 'most' of them, or not, as you can get into playing word-games
in English about the relationships between different 'infinity' values and
subtracting finite values from them or taking ratios. c.f. discussions in
H2G2 about how much it rains. Beyond that I'll leave the question for
mathematicians and other theologians. :-)

--
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Audio Misc http://www.audiomisc.co.uk/index.html
Armstrong Audio http://www.audiomisc.co.uk/Armstrong/armstrong.html