Multiwindow Gabor-type representations and signal representation by partial information (Q2772775)

The author reviews recent results concerning multiwindow Gabor-type representations and signal representations by partial information.NEWLINENEWLINENEWLINEThese results were obtained by the author et al. as well as by other researchers, e.g., Logan, Poggio et al., Cohen et al., Oppenheim and Hayes et al.. A good overview of the addressed topics gives the following table of contents.NEWLINENEWLINENEWLINE2. Multiwindow Gabor-type frames,NEWLINENEWLINENEWLINE2.1 Generalized Gabor-type schemes and the Zak transform,NEWLINENEWLINENEWLINE2.2 Multiwindow Gabor-type expansions,NEWLINENEWLINENEWLINE2.3 Matrix algebra approach for the analysis of frames properties,NEWLINENEWLINENEWLINE2.4 The Balian-Low theorem in the case of multi-windows,NEWLINENEWLINENEWLINE2.5 A wavelet-type Gabor scheme,NEWLINENEWLINENEWLINE3. Signal representation by partial information,NEWLINENEWLINENEWLINE3.1 Fourier and related transforms,NEWLINENEWLINENEWLINE3.2 Time and position domains -- zero crossings,NEWLINENEWLINENEWLINE3.3 Frequency domain -- discrete signals,NEWLINENEWLINENEWLINE4. Duality of results in time and frequency domains,NEWLINENEWLINENEWLINE4.1 Signal representation by its Fourier phase,NEWLINENEWLINENEWLINE4.2 Signal representation by its sampled Fourier phase,NEWLINENEWLINENEWLINE4.3 Derivation of Theorem 14,NEWLINENEWLINENEWLINE4.4 Signal representation by Fourier magnitude,NEWLINENEWLINENEWLINE4.5 Signal representation by Fourier signed-magnitude,NEWLINENEWLINENEWLINE4.6 Signal representation by one bit of Fourier phase,NEWLINENEWLINENEWLINE4.7 Signal and image reconstruction from localized phase.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00019].