Joel Kolstad wrote:
. . .
Say you start with a baseband FM signal. Let's call the two sides of its
Fourier transform L and R for the 'left' and 'right' halves. Now we mix up
to the desired carrier frequency. At -f_c we have L at even greater
negative frequencies and R at smaller negative frequencies. Ditto at f_c.
If we now apply a low pass filter to select the lower sideband, we end up
with R and L -- No information has been lost! (Likewise, with a high pass
filter you have L and R left -- Same deal.)

Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose
information. Yes, in practice we'll be talking about VSB instead of SSB,
but I still think we're OK.

I'm afraid you lost me with the "baseband" FM signal. Would you provide
a carrier frequency, modulation frequency, and deviation or modulation
index as an example?

The lower and upper sidebands of an FM signal do contain the same
information when the modulation is a single sine wave, even though the
sidebands aren't identical. But when you modulate with a complex
waveform, you might find that some of the information which is adding in
one sideband is subtracting in the other, and you might not be able to
recover the modulating waveform from only one or the other -- sort of
like you can't get two separate stereo channels from just the sum
signal. I don't know if that's true, but it wouldn't surprise me. And,
as I pointed out in another posting, the entire modulation information
isn't even contained in *both* sidebands except under very special
conditions -- some is in the carrier. Another question, of course, is
whether you can get close enough to be useful. Perhaps with NBFM, at
least, you could.

Speaking of narrowband FM (NBFM)... and at the risk of splitting this
topic... I had a discussion today with someone over the ability to use an
envelope detector to recover narrowband FM signals. The output of the
envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the
original modulating signal. The '1' will be killed by a capacitor, but that
leaves the cosine squared term... which seems impossible to easily change
back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that
we've irreversably lost information. Comments?

Cos^2(x) = abs(cos(x)) = 1/2 * (1 + cos(2x)). As you've noted, the DC
term can be blocked with a capacitor, so you'd end up with a cosine wave
at twice the frequency.

But I've never heard of trying to detect NBFM directly with an envelope
detector like you'd detect AM. The trick we used in ye olden tymes was
called "slope detection". You tuned the signal so it was on the edge of
the IF filter. The filter slope converted the FM to AM, which was then
detected with the normal AM envelope detector. If you tuned directly to
the carrier frequency, you didn't hear any modulation to speak of.

Roy Lewallen, W7EL