Term of Award

Spring 2008

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Yan Wu

Committee Member 1

David Stone

Committee Member 2

Goran Lesaja

Abstract

Sampling theory plays an essential role in the advancement of digital signal processing (DSP). All known DSP processors only work with digital samples of an analog signal (continuous-time signal). Therefore, reliable sampling of a signal is crucial for the successive phases of DSP. A well-known industry standard for sufficient sampling of an analog signal is that the sampling rate is at least twice the highest frequency of the signal. Obviously, the greater the highest frequency of the signal, the higher the sampling rate required, hence, more wear and tear on the sampling device. This research focuses on developing sampling methods for passband signals, which arises for broad-band signal processing, and it has drawn great interests in the DSP community. A first-order sampling method with optimal and total identification of all permissible sampling rates for two-band passband signals is studied in this work. A rigorous proof for all the sampling rates is presented. It is shown that the new sampling rates are much lower than the industrial standard. Therefore, the new sampling mechanism has sound theoretical and commercial values. Quantitative analysis is performed on the proposed sampling method, including a fast algorithm for computing all feasible sampling rates for two-band passband signals.

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