M.Tech (Signal Processing)
(To be applicable from July
2013-batch onwards)
|
Semester
I |
|||
|
Code |
Course
Name |
L–T-P |
Credit |
|
EE 501 |
Linear
Algebra and Optimization |
3-0-0 |
6 |
|
EE 504 |
Probability
and Stochastic Processes |
3-0-0 |
6 |
|
EE 524 |
Signal
Processing Algorithms and Architectures |
3-0-0 |
6 |
|
EE
5/6xx |
Elective
I |
3-0-0 |
6 |
|
EE
5/6xx |
Elective
II |
3-0-0 |
6 |
|
EE 528 |
Signals
and Systems Simulation Lab |
0-0-3 |
3 |
|
|
|
15-0-3 |
33 |
|
|
|||
|
Semester
II |
|||
|
Code |
Course
Name |
L-T-P |
Credit |
|
EE 525 |
Optimal
and Adaptive Signal Processing |
3-0-0 |
6 |
|
EE 636 |
Detection
and Estimation Theory |
3-0-0 |
6 |
|
EE
5/6xx |
Elective
III |
3-0-0 |
6 |
|
EE
5/6xx |
Elective
IV |
3-0-0 |
6 |
|
EE
5/6xx |
Elective
V |
3-0-0 |
6 |
|
EE 529 |
Digital
Signal Processors Lab |
0-0-3 |
3 |
|
|
|
15-0-3 |
33 |
|
Semester
III |
|||
|
Code |
Course
Name |
L-T-P |
Credit |
|
EE 698 |
Project
Phase I |
0-0-24 |
24 |
|
Semester
IV |
|||
|
Code |
Course
Name |
L-T-P |
Credit |
|
EE 699 |
Project
Phase II |
0-0-24 |
24 |
Credits: Course
– 66, Project – 48, Total – 114
|
Syllabi for M.Tech (Signal Processing) EE 501 Linear
Algebra and Optimization (3-0-0-6) 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 non-linear constraints, equality and
inequality constraints, optimality conditions, constrained convex
optimization, projected gradient methods, penalty methods. Texts / References:
EE
504
Probability
and Stochastic Processes
(3-0-0-6) 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, Borel-Cantelli Lemma; random variable: probability distribution, density and mass functions, functions of a
random variable; expectation, characteristic and moment-generating 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 mean-square
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 - strict-sense stationary
and wide-sense stationary (WSS) processes: time averages and ergodicity; spectral representation of a real WSS
process-power spectral density, cross-power spectral density, linear
time-invariant 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 (3-0-0-6) 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,
Sine-cosine 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 (0-0-3-3) 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; z-transform; 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, Monte-Carlo simulation. Applications:
Array Signal Processing, Communication Systems, Multirate
Signal Processing, Image Processing, Speech Processing. Texts/References:
EE
525 Optimal
and Adaptive Signal Processing
(3-0-0-6) Preamble: The
objective of the course is to provide an in-depth 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 wide-sense stationary inputs, spectral factorization theorem
and innovation processes, autoregressive moving average processes; Linear minimum mean-square error
(LMMSE) estimation: minimum mean-square error(MMSE) estimation of jointly
Gaussian random variables, LMMSE, orthogonality
principle and Wiener Hoff equation;
FIR Wiener filters, linear prediction-forward and backward
predictions, Levinson-Durbin Algorithm and lattice filter; IIR Wiener filters: non-causal Wiener
filter, innovation and and causal Wiener filter; Kalman filters: Gauss-Markov state variable models; innovation
and Kalman recursion, steady-state behaviour of Kalman filters;
Adaptive filters: steepest descent solution of FIR Wiener filter, LMS
algorithm- convergence, steady-state behaviour and
practical considerations, RLS algorithm- method of least-squares, recursive
solution and square-root algorithms, application of adaptive
filters-equalization 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 (0-0-3-3) 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 z-transform, 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
n-tuple 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 multi-media applications. Texts / References:
LIST OF ELECTIVES
FOR MTECH (SIGNAL PROCESSING)
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||