# 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

## 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.