FM Signals are demodulated on an entirely digital basis by converting the digitalized signal into a pair of signals which are substantially Hilbert transforms of each other. This requires at least one pair of nonrecursive filters having lower signal sample rates at the output than at the input. Each signal is delayed by one output sample interval, so that cross products of the delayed and undelayed Hilbert transforms can be formed, and the difference between them obtained. Finally, an arc-sine table is used to remove sine-function distortion. A single multiplier-accumulator provided with extra registers can perform all of the necessary arithmetical operations at the speeds required.