Introduction, motivation
and applications to multi-resolution signal processing and adaptive filtering.
Review of multi-rate signal processing, vector spaces, inner
products, Noble identities, multi-rate identities. Overview of wavelets,
STFT, Time-Frequency tiles, uncertainty principle (2 weeks)
Time domain, modulation domain, and
polyphase domain analysis of Perfect Reconstruction Filter Banks: projections
on to subspaces (1.5 weeks)
Daubechies’ filter design, spectral
factorization, Max-flat concept, vanishing moment properties. Wavelets
derived from filter banks. Multiresolution ladder of spaces; tree-structured
filter banks and wavelet packets (2 weeks)
Lifting constructions and non-uniform
sampling with filter banks. Sampling based on finite rate of innovations.
Applications of wavelets to signal denoising, compression, transmission.
(1.5 weeks)
Review of quantization concepts, brief
tutorial of Shannon quantization theory and waterfilling concepts.Introduction to the KLT.Properties of the KLT.Comparisons
with the DCT and wavelet transforms (1.5 weeks).
Wold-decomposition. Power-spectrum
& filtering of WSS process. MA, AR, ARMA models, Wiener filtering,
non-causal Wiener-Hopf equations, causal Wiener filter. Applications of
adaptive filtering to equalization, echo cancellation, interference cancellation.
(1.5 weeks)
LMS adaptive filters. First and second
order analysis.Practical variants of LMS
algorithm such as Normalized LMS, tap-weight leakage, frequency-domain
LMS, blind equalization and the Constant Modulus Algorithm (2 weeks).
RLS adaptive filters. Brief introduction
to the Kalman filter (time-permiting): (1 week).
Linear-Prediction.Levinson-Durbin fast
algorithm. Lattice-structures of forward-backward linear prediction (1.5
weeks).
DPCM and analysis.Applications to speech coding. (1 week).
References for background:
Some textbooks are on reserve in the engineering library.
General DSP:
A. V. Oppenheim and R. W. Schafer with John R. Buck, Discrete-time
Signal Processing, Second Edition, Prentice-Hall, 1999 Reserved
J. Proakis and D. Manolakis, Digital Signal Processing: Principles,
Algorithms, and Applications, 3rd edition, Prentice-Hall, 1996. Reserved
J.S. Lim and A. V. Oppenheim, Eds, Advanced Topics in Signal Processing,
Prentice-Hall, Englewood Cliffs, NJ, 1988
S. K. Mitra, Digital Signal Processing: A Computer-Based Approach,
McGraw Hill, 1998.
Adaptive filtering:
P.M. Clarkson, Optimal and Adaptive Signal Processing, CRC Press,
Boca Raton, FL, 1993. Reserved
B. Widrow and S. D. Stearns, Adaptive Signal Processing, Prentice-Hall,
1985
S. Haykin, Adaptive Filter Theory, 2nd Ed., Prentice-Hall, 1991.
Reserved
Statistical signal processing:
B. Porat, Digital Processing of Random Signals: theory and methods,
Prentice-Hall, 1994.
Monson Hayes, Stochastic Signal Processing, Prentice-Hall, 1996.
Reserved
Spectral analysis:
P. Stoica and R. Moses, Introduction to Spectral Analysis, Prentice-Hall,
Englewood Cliffs, NJ, 1997
S. M. Kay, Modern Spectral Estimation, Theory and Applications, Prentice-Hall,
Englewood Cliffs, NJ, 1988
Multirate signal processing and wavelets:
M. Vetterli and J. Kovacevic, Wavelets and subband coding, Prentice-Hall,
1995. Reserved
P. P. Vaidyanathan, Multirate systems and filter banks, Prentice-Hall,
1993. Reserved
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1998.
Quantization and coding
N. Jayant and P. Noll, Digital Coding of Waveforms, Prentice-Hall,
1984
A. Gersho and R. M. Gray, Vector quantization and signal compression,
Kluwer Academic Publishers, 1992.
Fast algorithms
R. Blahut, Fast algorithms for digital signal processing, Reading,
MA, Addison-Wesley, 1984. Reserved
Probability
A. Papoulis, Probability, Random Variables and Stochastic Processes,
McGraw-Hill, 1984.
A. Leon-Garcia, Probability and Random Processes for Electrical Engineering,
Addison-Wesley, 1993.
Linear algebra
Gilbert Strang, Linear Algebra and Applications, Academic Press, 1980.
Reserved
Policy: Homeworks are due two
weeks from the date they were assigned. Homework submissions will not be
returned so make a copy before turning them in. You are required to self-grade
your homeworks on the basis of the posted solutions and the following guideline.
Give each problem a zero if you got less than half the problem correct,
a one if you got most of it correct, and a half otherwise. You are required
to submit your grades for all problems one week from the day the solutions
are posted. A subset of homeworks will be picked at random and graded by the
reader.