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Signal Processing for Sparse Discrete Time Systems Open Access


Other title
Channel estimation
Compressive sampling
Analog-to-information conversion
Type of item
Degree grantor
University of Alberta
Author or creator
Taheri, Omid
Supervisor and department
Vorobyov, Sergiy A (Electrical and Computer Engineering)
Examining committee member and department
Jiang, Hai (Electrical and Computer Engineering)
Ardakani, Masoud (Electrical and Computer Engineering)
Sacchi, Mauricio (Department of Physics)
Cevher, Volkan (Ecole Polytechnique Federale de Lausanne)
Department of Electrical and Computer Engineering
Signal and Image Processing
Date accepted
Graduation date
Doctor of Philosophy
Degree level
In recent years compressive sampling (CS) has appeared in the signal processing literature as a legitimate contender for processing of sparse signals. Natural signals such as speech, image and video are compressible. In most signal processing systems dealing with these signals the signal is first sampled and later on compressed. The philosophy of CS however is to sample and compress the signal at the same time. CS is finding applications in a wide variety of areas including medical imaging, seismology, cognitive radio, and channel estimation among others. Although CS has been given a great deal of attention in the past few years the theory is still naive and its fullest potential is still to be proven. The research in CS covers a wide span from theory of sampling and recovery algorithms to sampling device design to sparse CS-based signal processing applications. The contributions of this thesis are as follows; (i) The analog-to-information converter (AIC) is the device that is designed to collect compressed samples. It is a replacement for the analog-to-digital converter in a traditional signal processing system. We propose a modified structure for the AIC which leads to reducing the complexity of the current design without sacrificing the recovery performance. (ii) Traditional parameter estimation algorithms such as least mean square (LMS) do not assume any structural information about the system. Motivated by the ideas from CS we introduce a number of modified LMS algorithms for the sparse channel estimation problem. Decimated LMS algorithms for the special case of frequency sparse channels are also given. (iii) At last we consider the problem of CS of two dimensional signals. The most straightforward approach is to first find the vector form of a two dimensional signal and then use traditional CS methods to collect the compressed samples. However, our approach samples all the columns of a two dimensional signal with the same measurement matrix. This leads to simplification of the sampling process and also enables us to perform parallel signal recovery.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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