On the Equivalence of Hanning-Weighted and Overlapped Analysis Windows Using Different Window Sizes

This letter is concerned with time-series analysis using overlapped processing windows shaded using the Hanning window function, such as is used in short-time Fourier transform (STFT) analysis. We present a special case where different analysis window sizes produce equivalent outputs where equivalence is defined by the existence of an orthonormal linear transformation relating the two analyses. We apply the concept to the problem of detecting pulses of unknown duration in Gaussian noise. We also demonstrate how the method can be used to apply the PDF projection theorem to shaded overlapped processing windows.