ECE 513 Textbooks and Useful Links

Text

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10

Lecture notes

• Notes on PCA and reference on The break point of signal subspace estimation
• Notes on Wiener Filtering
• Paper on fast steerable PCA
• Notes on sparse and low rank model
• Notes on steerable PCA and steerable exponential family PCA
• Introduction to Reproducible Kernel Hilbert Space

Recommended Texts

• Foundations of Signal Processing by Martin Vetterli, Jelena Kovacevic, and Vivek K Goyal, 2014.
• Fourier and Wavelet Representations by Martin Vetterli, Jelena Kovacevic, and Vivek K Goyal, 2013.
• T. Moon and W. Sterling, Mathematical Methods and Algorithms for Signal Processing, Prentice Hall, 2000.
• F. Deutsch, Best Approximation in Inner Product Spaces, Springer Verlag, 2001. (Recommended). Excellent book and good reference.
• A. W. Naylor and G. R. Sell, Linear Operator theory in Engineering and Science, Springer Verlag, 1982 (recommended). Excellent book for the Hilbert Space theory in the course.
• C.L. Byrne, Signal Processing, a Mathematical Approach, A.K Peters, 2005.
• P. Bremaud, Mathematical Principles of Signal Processing, Fourier and Wavelet Analaysis, Springer-Verlag, 2002.
• P. Stoica and R. L. Moses, Introduction to Spectral Analysis, Prentice Hall, 1997.
• B. Porat, Digital Processing of Random Signals: Theory and Methods, Prentice Hall, 1994.
• T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation, Prentice Hall, 2000.
• J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
• L. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.
• C. R. Vogel, Computational Methods for Inverse Problems, SIAM, 2002.
• G. Golub and C. Van Loan, Matrix Computations, Johns Hopkins University Press, 3rd ed. 1996.
• Singular Value Decomposition, Eigenfaces, and 3D Reconstructions by Muller, Magaia, and Herbst, in SIAM Review, Vol. 46, No. 3.
• Sparse and Redundant Representation: From Theory to Applications in Signal and Image Processing by Michael Elad, Springer, 2010.

No other question has ever moved so profoundly the spirit; no other idea has so fruitfully stimulated the intellect; yet no other concept stands in greater need of clarification than that of the infinite. David Hilbert

ECE 513 (Vector Space Signal Processing) covers mathematical tools in a vector space framework, including: finite and infinite dimensional vector spaces, Hilbert spaces, orthogonal projections, subspace techniques, least-squares methods, matrix decomposition, conditioning and regularizations, bases and frames, the Hilbert space of random variables, random processes, iterative methods; applications in signal processing, including inverse problems, filter design, sampling, interpolation, sensor array processing, signal and spectral estimation, sparse approximation and compressed sensing. Course Information: Prerequisite: ECE 310, ECE 313, and Math 415.

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