A Covariant, Discrete Time-Frequency Representation Tailored for Zero-Based Signal Detection

Recent work in time-frequency analysis proposed to switch the focus from maxima of spectrogram toward its zeros, which, for signals corrupted by Gaussian noise, form a random point pattern with very stable structure leveraged modern spatial statistics tools perform component disentanglement and signal detection. The major bottlenecks this approach are discretization Short-Time Fourier Transform boundedness observation window deteriorating estimation summary on which processing procedures rely. To circumvent these limitations, we introduce Kravchuk transform, generalized representation suited discrete signals, providing covariant numerically tractable counterpart recently compact phase space, particularly amenable statistics. Interesting properties transform demonstrated, among covariance under action SO(3) invertibility. We further show that process zeros white noise coincides those spherical Analytic Function, implying invariance isometries sphere. Elaborating theorem, develop procedure detection based spectrogram, whose statistical power is assessed intensive numerical simulations, compares favorably state-of-the-art zeros-based procedures. Furthermore it appears be robust both low signal-to-noise ratio small number samples.