I am trying to figure out what the carrier frequency of a signal is given only its discrete-time domain information and the fact that it is a signal on the AM radio frequency band(550 - 1700kHz). Is this possible? if so, how can I do it?
AM Broadcast is large carrier AM, in that the carrier is always present and the amplitude is modulated consistent with the waveform of interest. You can simply hard limit the signal to remove all amplitude modulation, leaving an unmodulated carrier from which it would be easy to derive the precise carrier frequency from any known reference of time.
This is basically, and as simply, just observing and averaging the times for the zero crossings of the waveform to determine the carrier frequency. Hard limiting can allow for lower estimation error In lower SNR conditions (but signal should be bandpass filtered first within the approximate carrier bandwidth to the extent that is known, as a strong out of band jammer could otherwise capture the limiter if it creates a negative SNR condition).
1$\begingroup$ This is a good pragmatic answer. If there was also noise (which might sometimes trigger extra zero crossings), the textbook answer might be a PLL operating on the hard-limited or even soft-limited AM signal. (again assuming it's not DSB-SC for "suppressed carrier".) $\endgroup$ Jun 28, 2021 at 3:26
1$\begingroup$ another possibility would be shaping the soft-limited AM signal to more of a sinusoid, using the Hilbert Transform and compute the one-sided analytic signal. The instantaneous phase can be derived and the derivative w.r.t. time calculated from that. In any case, LPF filtering the instantaneous frequency might be good. But you should get a solid value doing that. $\endgroup$ Jun 28, 2021 at 3:29
$\begingroup$ Thanks- good comments.. I do like the your second comment best since that would use every sample and not just the crossings so would be the most robust solution. I edited mine to add "averaging the time" but still I never really liked zero crossing measurements. $\endgroup$ Jun 28, 2021 at 3:32
$\begingroup$ There is a way to take the derivative of phase (w.r.t. time for instantaneous frequency and w.r.t. frequency for group delay) and avoid the need for phase unwrapping. I have this answer but I thought I had a more explicit answer. $\endgroup$ Jun 28, 2021 at 3:36
$\begingroup$ @robertbristow-johnson that would be interesting--- I also took up a debate with yours and Hilmar's position that instantaneous frequency only applies to narrow band signals. (I haven't thought all the way through the analytic signal but believe it would be the same thought process so was starting with Hilmar's statement in case you had a good explanation ----to my comment at that answer) $\endgroup$ Jun 28, 2021 at 3:45