Roy Lewallen wrote:
The amplitudes of the sideband components are symmetrical (at least for
modulation by a single sine wave), but the phases aren't. The phases of
all the upper sideband components are in phase with the carrier; in the
lower sideband, the odd order components (and only the odd order ones)
are reversed in phase.

I certainly didn't realize that until you pointed it out; I was generalzing
from the narrowband FM situation where only the first sideband components
are necessarily maintained and incorrectly assuming the same phase
differences applied to the general case.

However...

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.

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?

---Joel Kolstad
....ambitious novice who'll be licensed shortly...
....and I still think C-QUAM AM stereo is quite clever...