I was over on comp.dsp exposing my ignorance the other day when it eventually
dawned on me that a frequency multiplier will, in the frequency domain, just
convolve whatever the input signal is with itself. This got me to thinking...
why is it that frequency multipliers work as well as they do for something
like FM? Assuming a sine wave modulating signal, the FM spectra is a sum
harmonics with amplitudes dictated by a Bessel function; frequency multiplying
this would seem to add new harmonic content to the mix besides just doubling
the frequency of what's already present. So... does it turn out,
mathematically, that frequency multiplying an FM signal just so happens to end
up what nothing more than a "frequency scaled" spectra of what was originally
present? Or is some amount of distortion added in the process (assuming
perfect mixers used as the frequency multipliers and the DC component of the
mixers' outputs removed).

I've been told that, in general, frequency multiplier can be effectively
applied to most any modulation scheme that has a reasonably constant envelope,
e.g., FM, PM, FSK, even QPSK. Is this generally accepted knowledge?

Thanks,
---Joel Kolstad