Time-frequency localization and sampling of multiband signals
This survey paper presents results and open problems regarding sampling and time-frequency localization of multiband signals. This paper begins with a review of some classical work concerning essentially time- and bandlimited signals [see e.g. \textit{H. J. Landau}, IEEE Trans. Inf. Theory 39, No. 4, 1152--1156 (1993; Zbl 0808.94004)] and ends reviewing some work of \textit{E. Candès} and \textit{J. Romberg} [Inverse Probl. 23, No. 3, 969--985 (2007; Zbl 1120.94005)] that places probabilistic limitations on essential time- and bandlimiting for finite signals and their discrete Fourier transforms. In between the authors outline some connections from the continuous, singleband setting to the finite, multiband setting and pose some open problems. These connections involve time-frequency localization of multiband signals and sampling theory for such signals.
essentially time- and bandlimited signal
scientific article; zbMATH DE number 5636314
scientific article