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This paper analyzes the threshold characteristic of FM signals. An exact solution, obtained previously  for Gaussian base-band modulation, is generalized in order to obtain the autocorrelation function of the output signal plus noise of an FM discriminator for the case of more general baseband signals. For an application of the general results, sinusoidal modulation is analyzed in detail. It is shown that, under appropriate conditions, the heuristic result obtained by Rice  for sinusoidal modulation can be derived from the exact solution that is obtained here.