ON THE FALSE ALARM PROBABILITY FOR AN OVERLAPPED FFT PROCESSOR

A standard processor for detecting narrowband signals in noise applies the fast Fourier transform (FFT) to overlapped data blocks, and then suns the squared magnitudes of the bins from successive FFTs. The over lap of the data blocks causes these bins to be correlated, even when t he noise is white. A simple expression is derived for the probability of false alarm when the covariance matrix of the FFT bins is tridiagon al.