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).