You're probably thinking of AM vs. narrow band FM. Although the equations
look very similar on paper and the MAGNITUDE spectrum is identical, the
phase spectrum is different

Joel-

Perhaps that is what I'm remembering. Now, if you use a filter to eliminate
the other sideband, the higher frequency components and the carrier, don't you
have a nearly identical remainder?

See the message I posted earlier tonight for a discussion of whether or not
you can recover NBFM with an envelope detector

Somehow I missed that one. It seems that AOL does not post messages in the
order in which they were originated!

I think we are in agreement that you can't recover FM modulation with just an
envelope detector, but there is another approach. Again, you need a filter,
but maybe one that is not as sharp as above. If you tune the radio so the
carrier is just outside the passband, an amplitude variation will occur as the
signal slides up and down the shoulder of the filter. The result is a pseudo
AM signal that is detected by the envelope detector. I recall that this
approach is called "slope detection".

73, Fred, K4DII