MSc.  in Electrical Communication Engineering                                                     (Aug/1999 - Jan/2002)
Department of Electrical Communication Engineering
Indian Institute of Science, Bangalore, INDIA
 

Credit Courses:

Course No.  Credits     Term           Course Name                                           Instructor

MA 221          3:0          Aug/1999     Linear Algebra                                         A. V. Gopalakrishna
E9 213           3:0           Aug/1999    Time-Frequency Analysis                           G. V. Anand
E9 221           3:0           Aug/1999    Digital Signal Compression                      T. V. Sreenivas
E9 241           2:1           Aug/1999    Digital Image Processing                         A. G. Ramakrishnan
E9 242           3:0           Aug/1999    Special Topics in Image Processing          K. R. Ramakrishnan
E1 244           3:0           Jan/2000     Estimation Identification & Modelling     G. V. Anand

Linear Algebra

Vector Spaces-subspaces-Linear independence-Basis-Dimension. Direct sum of subspaces. Linear system of equations-Row reduced echelon form of a matrix-null space and range of a matrix-solutions of nonhomogeneous systems-row space, column space, row rank, column rank, rank. Nullity theorem. Linear transformations -representation of a linear transformation by a matrix - change of basis - Null space and range, rank-nullity theorem. Relation between null space and range of a matrix and its transpose -least square and optimal solutions - eigenvectors Diagonalizability criteria. Hermitian matrices - eigenvalues and eigenvectors of hermitian matrices - diagonalizability. Nonnegative matrices singular values and singular value Decomposition pseudoinverse. Invariant subspaces, invariant direct sum decomposition - primary decomposition theorem - Nilpotent matrices - Jordan canonical form.
References
Hoffman, K. and Kunze, R., Linear Algebra, Prentice-Hall, 1970.
Halmos, P. R., Finite Dimensional Vector Spaces, Van Nostrand, 1974.
Strang, G., Linear Algebra and Its Applications, Saunders, 1988.

Frequency analysis, Short time Fourier transform, uncertainty principle, Wavelet transform, frames, wavelet series.  ultiresolution analysis, scaling functions and wavelets. Haar, sine and spline wavelets. Iterated filter banks. Construction of capacity supported wavelets. Wavelet packets, bilinear time frequency distribution, Wigner distribution, general Cohen’s class. Kernel and characteristic function of TFD’s, Kernel design for reduced interference. Positive distributions.
References
Cohen L., Time-Frequency Analysis, Prentice-Hall, 1995.
Burrus C.S., Gopinath R.A., and Guo H., Wavelets and Wavelet Transforms, Prentice-Hall, 1998.

Speech and Image Waveform Characterization - Source Models, Quantization - Optimal and Adaptive Quantiztion, Predictive Coding: DPCM, Linear Prediction, Prediction for video, Adaptive Prediction, DM, ADM; Transform Coding: Orthogonal Transoforms, Bit Allocation, Perceptual criteria, Subband Coding Vector Quantizaqtion: Optimal VQ, Multistage VQ, TSVQ data compression: Entropy coding-Huffman, Run-length, Arithmetic and Ziv-Lempel coding.
References
Jayant N.S., and Noll P., Digital Coding of Waveforms-Principles and Application to Speech and Video,Prentice Hall, 1984.
Gersho A, and Gray R, ”Vector Quantifisation and Signal Compression” Kulwer Acad Publication.

Introduction to Human Visual System & Machine vision systems, Basic Mathematical concepts, Introduction to Digital Image Fundamentals, Imaging geometry, stereo imaging, Introduction to Light & Color science, Frequency domain representation of signals, 2D Unitary transforms and their properties, Image Filtering, spatial and frequency domain techniques, Image Segmentation, Image coding/compression, Image Representation & Description, Pattern Recognition & Image Interpretation, Space-Frequency analysis for Images Neural Networks in Image Processing Medical Image Processing and Challenges, Document analysis: OCR system, Video Processing, Other Image Processing Issues, Challenges & future directions
References
Digital Image Processing; Gonzalez & Woods; Addison Wesley.
Fundamentals of Digital Image Processing; A K Jain; PHI.
Image Processing, Analysis, and Machine Visions; Sonka et. al.; PWS Publishers, 2nd Edn.

Introduction to Wavelets, Discrete Wavelet Transform, Multiresolution Analysis, Wavelet construction, Picture coding and compression - wavelet methods, Wavelet based image denoising.

References
Recent Papers from image processing literature

Hypothesis testing, Neyman-Pearson theorem, LRT and GLRT, UMP test, multiple-decision problem, detection of deterministic and random signals in noise. Parameter Estimation: Unbiasedness, consistency asymptotic normality, sufficient statistics, minimax estimation, Rao-Blackwell theorem, Cramer-Rao bound. Method of obtaining estimators: Method of moments, maximum liklihood, Bayes estimators. Minimum mean square error linear estimation: Wiener filter, Kalman filter, levinson-Durbin and innovation algorithm. Time series: basics; second order process, autocorrelation
function, ARNA (p,q) processes, invertibility, casuality, spectral representation. Estimation of mean, auto covariance, parameters of ARMA modeling coefficients, spectral density. Identification: ARMA models, AIC criterion.
References
Kay, Stevens M., Fundamentals of Staistical Signal Processing, Vol. 1 and 23, Prentice Hall, 1993, 1998
Brookwell, P. J., and Davis, R. A., Time Series: Theory and Methods, Springer 1987.
 

Course No.  Credits     Term           Course Name                                           Instructor
MA 223        3:0            Jan/2000     Functional Analysis                                   Vittal Rao
E9 202          3:0            Jan/2000    Advanced Digital Signal Processing         Anamitra Makur
MA 221        3:0            Aug/2000    Analysis - 1                                                Mithily Ramaswamy

Functional Analysis

Basic topological concepts, Metric spaces, Normed linear spaces, Banach spaces, Bounded linear functionals and dual spaces, Hahn Banach Theorem, Bounded linear operators, Open mappingtheorem  closed graph theorem, Banach-Steinhaus theorem, Orthonormal sets, Orthogonal complements, bounded operators on a Hilbert space up to the spectral theorem for compact, self - adjoint operators.
References
Conway, J. B., A course in Functional Analysis, Springer, 1990.
Taylor, A.E., Introduction to Functional Analysis, Wiley International Edition, 1958.
Bachman, G. and Narici, L., Functional Analysis, Academic press, 1966.

Basic multirate operations, polyphase repre-sentation, multistage implementations. A simple aliasfree QMF system, perfect reconstruction (PR) systems, tree structured filter banks. Two channel FIR paraunitary QMF banks, M-channel FIR paraunitary filter banks. Lattice structures for linear phase FIR PRQ MF banks. cosine modulated filter banks, design of the pseudo QMF bank, efficient polyphase structures. The wavelet transform and its relation to multirate filter banks. Subband coding and coding gain. Two-dimensional filter banks.
References
Vaidyanathan P.P, Multirate Systems and Filter Banks, Prentice Hall, 1983.
Filege N.J., Multirate Digital Signal Processing John wiley & sons, 1994.

Review of Real and complex numbers systems, Topology of R, Continuity and differentiability, Mean value theorem, Intermediate value theorem, Implicit function theorem, Inverse function theorem, sequence and series of functions, Uniform convergence, Riemann-Stieltjes integral.
References
Rudin, W., Principles of Mathematical Analysis, McGrawHill, 1985.
Apostol, T.M., Mathematical Analysis, Narosa, 1987.