Frequency spectrum of signal sampled in modulation domain

There is complete sampling theory in time domain and frequency domain, sampling in the modulation domain is a new interesting topic. Mathematical analysis and simulation based on FSK signals reveal the rule: If we sample a signal in the modulation domain with rate f_ms, the frequency spectrum will extend periodically at the interval f_ms, which means harmonics will appear. And further measurement validates the rule. The rule will help to construct a more complete sampling theory contain "time domain", "frequency domain" and "modulation domain".