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 sums the squared magnitudes of the bins from successive FFTs. The overlap of the data blocks causes these bins to be correlated, even when the noise is white. A simple expression is derived for the probability of false alarm when the covariance matrix of the FFT bins is tridiagonal.