2018/08/20 by Franz Luef, Luef, Franz, Eirik Skrettingland +1 · 2 citations
Medicine · Mathematics · Computer Science · #ECG Monitoring and Analysis #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods
paper · pdf · doi:10.48550/arxiv.1808.06419
Recently we introduced mixed-state localization operators associated to a\ndensity operator and a (compact) domain in phase space. We continue the\ninvestigations of their eigenvalues and eigenvectors. Our main focus is the\ndefinition of a time-frequency distribution which is based on the Cohen class\ndistribution associated to the density operator and the eigenvectors of the\nmixed-state localization operator. This time-frequency distribution is called\nthe accumulated Cohen class distribution. If the trace class operator is a\nrank-one operator, then the mixed-state localization operators and the\naccumulated Cohen class distribution reduce to Daubechies' localization\noperators and the accumulated spectrogram. We extend all the results about the\naccumulated spectrogram to the accumulated Cohen class distribution. The\ntechniques used in the case of spectrograms cannot be adapted to other\ndistributions in Cohen's class since they rely on the reproducing kernel\nproperty of the short-time Fourier transform. Our approach is based on quantum\nharmonic analysis on phase space which also provides the tools and notions to\nintroduce the analogues of the accumulated spectrogram for mixed-state\nlocalization operators; the accumulated Cohen's class distributions.\n