Universal minimum-rate sampling and spectrum-blind reconstruction for multiband signals.

摘要

Various aspects concerning the proposed theory of spectrum-blind sampling of multi-band signals and related pattern and algorithm design issues are investigated in this dissertation. Traditionally, sampling pattern design and signal reconstruction fully depend on the knowledge of spectral support. In contrast, our approach assumes minimal knowledge about the spectral support (i.e., spectral occupancy rate and end-points of the spectral span, but not band structure, which has been vital for traditional approaches), thus enabling potential applications in diverse fields from data compression to Fourier imaging, to array processing and communications, which may not have been possible.;As far as we know, all work to date is still concentrated on spectral support dependent reconstruction, although the universality of the ill-conditioned bunched sampling pattern has been mentioned. Our approach combines well-conditioned universality, alias-resolving capability and spectrum-blind reconstructibility, and is capable of approaching the Landau-Nyquist minimum sampling rate, closing a fundamental gap in the Shannon sampling theory in the treatment of the widely used general class of multiband signals.;The dissertation includes three parts: (1) one-dimensional theory and design, (2) two-dimensional theory and design (which is readily extendable to higher dimensions), and (3) application to Fourier imaging. The proposed spectrum-blind sampling and reconstruction theory addresses issues like existence and optimal design of universal sampling patterns and their conditioning, algorithms and uniqueness conditions for optimal spectral support recovery, as well as algorithms, uniqueness conditions and other properties of signal reconstruction via a multiresolution approach. The investigations are conducted in the framework of the proposed multicoset sampling theory, employing a periodic nonuniform sampling pattern and noniterative multirate reconstruction schemes that combine the capability of nonuniform sampling and the ease of implementation of uniform sampling.