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An interesting problem.
From what I know, if conventional Demodulation techniques are used for demodulating AM and FM, the demodulation of one Modulation results in the loss of the other modulation technique. This eliminates cascading demodulation techniques.
Therefore, both Modulations should be de-modulated at the same time, by feeding the same signal to both the demodulating circuits.
1) Use an Amplitude detector (low pass filter) for Amplitude Demodulation
2) A Phase Shift Detector or any other Frequency demodulation techniques.
the signal is being genrated from a modulated disc.which comprises of transparent and opaque slots.at the back of the disc i have detectors.the light source is reflected via lens on to disc and you have a gyro which causes the light to be projected on to disc in a circular path.i am doing simulating this in matlab.my carrier freq is the product of number of slots and the freq with which the source is rotating.the position of the source can be found using the fm demodulation of the detected signal.its an example of a very narrow band fm demodulation.now the problem is the if my source is such that for a portion of time my sourcs gets off the disc.i get a dead zone in my signal.this can be regarded as AM.in such a case the wave detected by the detector happens to be both AM and FM.now i need to demodulate this wave.any suggestions???
If I understand well your problem, a PLL with lock detector could do the job.
Another possibilty is an all-digital system that measures pulse duration.
I don't see clearly whether you need to know speed or position.