Detection performance of an FM correlator

The detection performance of an FM correlator -the filtered product of two limiter-discriminator outputs-is assessed for a sinusoidal input signal with zero-mean Gaussian frequency modulation in Gaussian noise. Probabilities of detection and false alarm are obtained which depend upon carrier-to-noise ratio; modulation power; noise, modulation, and filter bandwidths; inter-channel delay; and observation time. Modulation and noise spectra are assumed Gaussian-shaped, and three filters are modelled: integrate-and-dump, RC integrator, and two-pole Butterworth.