Detection of Narrow-Band Frequency Modulated Signal

The detection of a narrow-band frequency modulated signal in the presence of white Gaussian noise is investigated. Using NeymanPearson criteria, it has been shown that the receiver is similar to the matched filter and performance of the receiver is also identical to the binary detection of known Signals in the presence of white noise, it is assumed in the anlaysis that the signal to noise ratio is very small and that the amplitude of the sinusoidal modulating signal is also very small.