In article , "Joel Kolstad"
writes:

Avery Fineman wrote:
There isn't any corresponding similarity of
FM and PM to AM for the repetition of sidebands' information when
looking at the spectral content.

Umm... last I looked the spectrum of FM and PM was symmetrical about the
carrier frequency? (Well, the lower sideband is 180 degrees out of phase
with the upper, but that's true of AM as well.) Looking at a single sine
wave input to an FM or phase modulator, this comes about from the Bessel
function expansion of the sidetones and J-n(x)=-Jn(x)?

Yes. More or less.

I know you're far more experienced in this area than I am, however, so I'll
let you explain what I'm misinterpreting here!

Noooo...I'm not going to. About a million subjective years ago I had to
slog through a solution and series expansion with the only "help" I got
being a suggestion to use Bessel Functions of the First Kind.

In doing so - AND thinking about it in the process - I learned quite a
bit about the math AND the modulation process. Very useful later on.
ALL learning takes place in one's own noggin...doesn't matter whether
one is in a formal class or alone being "lectured" by print on paper
through the eyeballs.

Over on the Agilent website, I would suggest downloading their free
Application Note 150-1. That is really a subtle selling thing for their
very fine spectrum analyzers but it is also a darn good treatise on
modulation and modulation spectra for all the basic types. It should
(unless altered there) include that nice little animated display of
sidebands versus modulation index. I've always admired those H-P
appnotes, valuing most as nice little tutorials on specialized subjects.

Richard Slater in the mentioned January '77 HR article was trying to
explain a combination of FM and AM. In order to get a proper "feel"
for that (in my opinion), one needs the experience of juggling those
series terms in the expanded equation form. There IS one hint and
that is the not-quite symmetry (in numeric values) of FM and PM
spectra as compared to AM spectra. True "single-sideband" has a
possibility only on true symmetry. FM and PM spectra, by
themselves, don't have that symmetry in the expanded form. I'm
not going to discuss that one since it should be apparent.

If you want some source code on calculating the numeric values of
Bessel Functions of the First Kind, I'll be happy to post it here under
some thread. It's short and not complicated and a #$%^!!! faster than
slugging through 5-place tables with slide rule and/or four-function
mechanical calculator. Been there, done too much of that. Computers
aren't just for chat rooms, are very nice for numeric calculations of the
large kind. :-)

Len Anderson
retired (from regular hours) electronic engineer person