I have a raw signal which, if interpreted correctly with various 'tuning' parameters set to their optimum values, can be seen to consist of a relatively small (but a priori unknown) set of discrete frequency components. With the tuning parameters set at sub-optimum values, the power spectrum is spread out - each frequency component is broader or, in the very poorly-tuned case, there can be many 'false' frequency peaks. Some example plots would be:
What I'd like is to be to able to auto-tune by identifying a figure-of-merit which is highest for the 'good tuning' case, lowest for the 'awful tuning' case, and somewhere in the middle for the 'poor tuning' case. If I knew a priori that there was a single frequency component, this would be fairly straightforwrad but I haven't been able to think of a good appraoch when the number of components is unknown.
Is there a standard approach to this problem that I'm unaware of?