M.Tech (Signal Processing)
(To be applicable from July
2013batch onwards)
Semester
I 

Code 
Course
Name 
L–TP 
Credit 
EE 501 
Linear
Algebra and Optimization 
300 
6 
EE 504 
Probability
and Stochastic Processes 
300 
6 
EE 524 
Signal
Processing Algorithms and Architectures 
300 
6 
EE
5/6xx 
Elective
I 
300 
6 
EE
5/6xx 
Elective
II 
300 
6 
EE 528 
Signals
and Systems Simulation Lab 
003 
3 


1503 
33 


Semester
II 

Code 
Course
Name 
LTP 
Credit 
EE 525 
Optimal
and Adaptive Signal Processing 
300 
6 
EE 636 
Detection
and Estimation Theory 
300 
6 
EE
5/6xx 
Elective
III 
300 
6 
EE
5/6xx 
Elective
IV 
300 
6 
EE
5/6xx 
Elective
V 
300 
6 
EE 529 
Digital
Signal Processors Lab 
003 
3 


1503 
33 
Semester
III 

Code 
Course
Name 
LTP 
Credit 
EE 698 
Project
Phase I 
0024 
24 
Semester
IV 

Code 
Course
Name 
LTP 
Credit 
EE 699 
Project
Phase II 
0024 
24 
Credits: Course
– 66, Project – 48, Total – 114
Syllabi for M.Tech (Signal Processing) EE 501 Linear
Algebra and Optimization (3006) Preamble: The
objective of this course is to provide a firm foundation in linear algebra
and optimization appropriate at the graduate level. The focus is both on
theoretical developments of ideas as well as algorithms. Course
Contents: Linear
Algebra  vector spaces, linear independence, bases and dimension, linear
maps and matrices, eigenvalues, invariant
subspaces, inner products, norms, orthonormal
bases, spectral theorem, isometries, polar and
singular value decomposition, operators on real and complex vector spaces,
characteristic polynomial, minimal polynomial; optimization  sequences and
limits, derivative matrix, level sets and gradients, Taylor series;
unconstrained optimization  necessary and sufficient conditions for optima,
convex sets, convex functions, optima of convex functions, steepest
descent, Newton and quasi Newton methods, conjugate direction methods;
constrained optimization  linear and nonlinear constraints, equality and
inequality constraints, optimality conditions, constrained convex
optimization, projected gradient methods, penalty methods. Texts / References:
EE
504
Probability
and Stochastic Processes
(3006) Preamble: The
objective of this course is to provide a solid foundation in probability and
stochastic processes appropriate at the graduate level. The examples will
emphasize applications in engineering, especially in signal processing and
communication engineering. Course
Contents: Axiomatic
definitions of probability; conditional probability, independence and Bayes theorem, continuity property of probabilities, BorelCantelli Lemma; random variable: probability distribution, density and mass functions, functions of a
random variable; expectation, characteristic and momentgenerating functions;
Chebyshev, Markov and Chernoff
bounds; jointly distributed random variables: joint distribution and density functions,
joint moments, conditional distributions and expectations, functions of
random variables; random vector mean vector and covariance matrix, Gaussian
random vectors; sequence of random variables: almost sure and meansquare
convergences, convergences in probability and in distribution, laws of large
numbers, central limit theorem; random process: probabilistic structure of a
random process; mean, autocorrelation and autocovariance
functions; stationarity  strictsense stationary
and widesense stationary (WSS) processes: time averages and ergodicity; spectral representation of a real WSS
processpower spectral density, crosspower spectral density, linear
timeinvariant systems with WSS process as an input time and frequency
domain analyses; examples of random processes: white noise, Gaussian, Poisson
and Markov processes. Texts / References
EE 524 Signal Processing Algorithms and
Architectures (3006) Preamble: The objective of the course is to quickly
review the foundational material covered in undergraduate level courses in
signal processing and present the key ideas in modern digital signal
processing. Emphasis will also be on implementation aspects of signal
processing algorithms on modern digital signal processors. Course
Contents: Orthogonal
transforms: DFT, DCT and Haar; Properties of DFT;
Computation of DFT: FFT and structures, Decimation in time, Decimation in
frequency; Linear convolution using DFT; Digital filter structures: Basic
FIR/IIR filter structures, FIR/IIR Cascaded lattice structures, Parallel allpass realization of IIR transfer functions,
Sinecosine generator; Computational complexity of filter structures; Multirate signal processing: Basic structures for
sampling rate conversion, Decimators and Interpolators; Multistage design of
interpolators and decimators; Polyphase
decomposition and FIR structures; Computationally efficient sampling rate
converters; Arbitrary sampling rate converters based on interpolation
algorithms: Lagrange interpolation, Spline
interpolation; Quadrature mirror filter banks;
Conditions for perfect reconstruction; Applications in subband
coding; Digital Signal Processors introduction: Computational characteristics
of DSP algorithms and applications; Techniques for enhancing computational
throughput: Harvard architecture, parallelism, pipelining, dedicated
multiplier, split ALU and barrel shifter; TMS320C64xx architecture: CPU data
paths and control, general purpose register files, register file cross
paths, memory load and store paths, data address paths, parallel operations,
resource constraints. Texts / References:
EE
528
Signals and Systems
Simulation Lab (0033) Preamble: This
is a simulation laboratory for ideas in signals and systems using MATLAB /
SCILAB / OCTAVE. Course
Contents: Fundamentals: Generation of signals, study
of system properties; convolution and correlation; ztransform; DFT using
FFT; Linear convolution using circular convolution; aliasing due to sampling
in time and frequency domains; Design of FIR and IIR filters; Estimation of
power spectral density using periodogram and
Welch's method; Generation of discrete and continuous random variables,
statistical analysis and validation, MonteCarlo simulation. Applications:
Array Signal Processing, Communication Systems, Multirate
Signal Processing, Image Processing, Speech Processing. Texts/References:
EE
525 Optimal
and Adaptive Signal Processing
(3006) Preamble: The
objective of the course is to provide an indepth treatment of algorithms in
optimal and adaptive signal processing. The course will cover topics in
random signals and optimal processing, algorithms and structures for adaptive
filtering and spectral analysis. Course
Contents: Review:
Hilbert space of random variables; response of linear systems to widesense stationary inputs, spectral factorization theorem
and innovation processes, autoregressive moving average processes; Linear minimum meansquare error
(LMMSE) estimation: minimum meansquare error(MMSE) estimation of jointly
Gaussian random variables, LMMSE, orthogonality
principle and Wiener Hoff equation;
FIR Wiener filters, linear predictionforward and backward
predictions, LevinsonDurbin Algorithm and lattice filter; IIR Wiener filters: noncausal Wiener
filter, innovation and and causal Wiener filter; Kalman filters: GaussMarkov state variable models; innovation
and Kalman recursion, steadystate behaviour of Kalman filters;
Adaptive filters: steepest descent solution of FIR Wiener filter, LMS
algorithm convergence, steadystate behaviour and
practical considerations, RLS algorithm method of leastsquares, recursive
solution and squareroot algorithms, application of adaptive
filtersequalization and noise cancellation. Spectral Estimation: Smoothed
and windowed periodograms, minimum variance,
maximum entropy and parametric methods for spectral estimation, frequency
estimation. Texts / References
EE 529 Digital Signal Processors
Lab (0033) Preamble: This
is a hardware laboratory using Texas Instruments TMS320C64xx kits to teach
implementation of fundamental signal processing algorithms. Course
Contents: Fundamentals:
Familiarization to Code Composer Studio; development cycle on TMS320C64xx
kit; Generation of signals, Fourier representation and ztransform, sampling theorem
in time and frequency domains, convolution and correlation, DFT and FFT; FIR
and IIR filters; sampling rate converters. Applications: Adaptive filter and
experiments on communication such as generation of a
ntuple PN sequence, generation of a white noise
sequence using the PN sequence, restoration of a sinusoidal signal embedded
in white noise by Wiener Filtering; speech and multimedia applications. Texts / References:
LIST OF ELECTIVES
FOR MTECH (SIGNAL PROCESSING)
