The total PFA of the multiwindow harmonic detector and its application to real data

The authors study the multiwindow spectral analysis method as it applies to the detection of sinusoidal signals. They examine the probability of false alarm P_FA. The total P _FA (sinusoidal frequency unknown) is shown analytically to be bounded below by the order statistics (minimum) of BM/K independent identically distributed (i.i.d.) beta variates, where M is the length of the data record used in the detection, K the number of windows, and B the width of the frequency band of interest. Simulation results indicate a much larger bound, the minimum of BM i.i.d. beta variates. It is shown that for real signals, the assumptions made in the derivation of the detector break down at frequencies close to zero and to half the sampling frequency