Theoretical Insight in the Recent Design Methodology of an Advanced Optimal Space/Spatial-Frequency Filter

Recently, a design methodology of an optimal space/spatial-frequency (S/SF) filter has been proposed. It is based on the filter’s region of support symmetrical extension around the detected local frequency (LF) of the estimated signal and on the spectral thresholding. Extension is performed by one-by-one including of groups of S/SF points having equally distance and the symmetrical distribution regarding the detected LF. However, the methodology has only empirically been considered. Here, we give the theory insight and prove that the considered methodology provides, with the probability substantially higher that the possible competitive methodologies, extension of the filter’s region of support up to the position projected by the predefined spectral threshold.