ECE 513/Links

ECE 513 Textbooks and Useful Links


Lecture notes

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.

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.