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Frequency modulation or FM is more complex. It has numerous advantages over AM, such as better fidelity and noise immunity. However, it is much more complex to both modulate and demodulate a carrier wave with FM, and AM predates it by several decades.
There are several common types of FM demodulator:
The quadrature detector, which phase shifts the signal by 90 degrees and multiplies it with the unshifted version. One of the terms that drops out from this operation is the original information signal, which is selected and amplified.
The phase-locked loop.
The most common is a Foster-Seeley discriminator. This is composed of an electronic filter which decreases the amplitude of some frequencies relative to others, followed by an AM demodulator. If the filter response changes linearly with frequency, the final analog output will be proportional to the input frequency, as desired.
Another method uses two AM demodulators, one tuned to the high end of the band and the other to the low end, and feed the outputs into a difference amp.
Another is to feed the signal into a phase-locked loop and use the error signal as the demodulated signal.
Ratio detector [2]
Using a digital signal processor, as used in software-defined radio.

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Frequency modulation or FM is more complex. It has numerous advantages over AM, such as better fidelity and noise immunity. However, it is much more complex to both modulate and demodulate a carrier wave with FM, and AM predates it by several decades.
There are several common types of FM demodulator:
The quadrature detector, which phase shifts the signal by 90 degrees and multiplies it with the unshifted version. One of the terms that drops out from this operation is the original information signal, which is selected and amplified.
The phase-locked loop.
The most common is a Foster-Seeley discriminator. This is composed of an electronic filter which decreases the amplitude of some frequencies relative to others, followed by an AM demodulator. If the filter response changes linearly with frequency, the final analog output will be proportional to the input frequency, as desired.
Another method uses two AM demodulators, one tuned to the high end of the band and the other to the low end, and feed the outputs into a difference amp.
Another is to feed the signal into a phase-locked loop and use the error signal as the demodulated signal.
Ratio detector [2]
Using a digital signal processor, as used in software-defined radio.