There isn't muchin this. Here is a brief explanation. Consider a signal
f(t) which represents an instantaneous frequency of a sinusoid and which carries some information. Then you can generate the signal phi(t) = 2 * pi* K * int_0^t f(tau) dtau which is the instantaneous phase (since it is an integral of f(t)) with some frequency gain K. Now you can form the complex exponential baseband signal s(t) = exp( j phi(t) ) and transmit it. This is the basis of FM modulation. Now imagine doing the above in discrete time. You would have something like f_k = f(k Ts) phi_k = phi(k Ts) ~= 2 * pi* K * sum_i=0^k f(i Ts) Ts = phi_{k-1} + 2 * pi * K * Ts * f_k (1) and finally s_k = exp(j phi_k) (2) The FM modulator block in GNURADIO does exactly that, ie equations (1) and (2) with sensitivity = 2 * pi * K * Ts The quadrature demodulator block in GNURADIO extracts phi_k from s_k (or from any complex signal for that matter) and multiplies with some irrelevant gain M so you get M * phi_k I hope this help, Achilleas
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