Division Approximation In Fm Demodulator

Another demod option I did 20 years ago is to take the Q/I as sin/cos and compute an arctan(sin/cos) to determine phase. I'd use a cordic for the arctan. You only need the quotient for this value. This gives you a PM demod by the way.

The next step is to take the difference between phase samples x[n] - x[n-1] which gives you a dθ/dt which is proportional to frequency offset. The frequency value is then equal to ± half the sample rate. For instance, with a 100MHz sample rate your demod range would cover ±50MHz. If this is wider than necessary you can insert pipeline stages between the subtraction terms such then your FM term is now x[n] - x[n-1-m] and now your demod range is ±50MHz/m.