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Algorithm To encode a signal $x_m$ in a carrier with frequency $f_c$, we proceed as: $$ y(t) = \cos(\phi(t)), \\ \phi(t) = 2\pi \cdot \left(f_c t + f_\Delta \int_0^t x_m(\tau)d\tau \right) $$ where $f_\Delta$ controls the maximum deviation of $y$'s instantaneous frequency from $f_c$ (effectively its bandwidth, but not in strict Fourier sense). Discrete-time ...


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The magnitude of the FFT will likely scale by the number of samples N depending on the specific algorithm you use. So the IFFF will be 1/N. Just multiply your FFT bins by N to normalize it. If you use any windowing this will change the result accordingly


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