ee325 probability and random processes

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    EE325 Probability and Random Processes

    Sets and set operations; Probability space, Conditional probability and Bayes theorem,Combinatorial probability an

    sampling models, Discrete random variables, probability mass function, probability distribution function, examplerandom variables and distributions, Continuous random variables, probability density function, probability

    distribution function, example distributions, Joint distributions, functions of one and two random variables, momen

    of random variables, Conditional distribution, densities and moments, Characteristic functions of a random variablear!ov, Chebyshev and Chernoff bounds; "andom se#uences and modes of convergence $everywhere, almost

    everywhere, probability, distribution and mean s#uare%, &imit theorems, Strong and wea! laws of large numbers,

    central limit theorem'"andom process' Stationary processes' ean and covariance functions'(rgodicity'

    )ransmission of random process through &)*' Power spectral density'Text/References

    +'Star! and J' oods,--Probability and "andom Processes with .pplications to Signal Processing,// )hird

    (dition, Pearson (ducation' $*ndian (dition is available%'

    .' Papoulis and S' 0nni!rishnan Pillai, --Probability, "andom 1ariables and Stochastic Processes,// 2ourth

    (dition, c3raw +ill' $*ndian (dition is available%'

    4' &' Chung, *ntroduction to Probability )heory with Stochastic Processes, Springer *nternational Student

    (dition'

    P' 3' +oel,S' C'Port and C'J' Stone *ntroduction to Probability, 0BS Publishers,l

    P' 3' +oel, S' C' Port and C' J' Stone, *ntroduction to Stochastic Processes,0BS Publishers

    S' "oss, *ntroduction to Stochastic odels, +arcourt .sia, .cademic Press'

    EE601 Statistical Signal Analysis

    "eview of probability theory and random variables5 )ransformation $function% of random variables, Conditional

    expectation;Se#uences of random variables5 convergence of se#uences of random variables';Stochastic processes5

    wide sense stationary processes, orthogonal increment processes, iener process, and the Poisson process, 4&expansion'; (rgodicity, ean s#uare continuity, mean s#uare derivative and mean s#uare integral of stochastic

    processes'; Stochastic systems5 response of linear dynamic systems $e'g' state space or .". systems% to stochastinputs, &yapunov e#uations, correlational function, power spectral density function, introduction to linear leasts#uare estimation, iener filtering and 4alman filtering'

    Text/References

    .' Papoulis, Probability, "andom 1ariables and stochastic processes, 6nd (d', c3raw +ill, 789:'

    .' &arson and B'' Schubert, Stochastic Processes, 1ol'* and **, +olden'

    EE60 Ada!ti"e Signal Processing

    "eview of linear and non'

    B' idrow and S'D' Stearns, .daptive signal processing, Prentice +all, 789@'

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    EE610 #mage Processing

    *mage representation < 3ray scale and colour *mages, image sampling and #uanti?ation';)wo dimensionalorthogonal transforms < D2), 22), +), +aar transform, 4&), DC)';*mage enhancement < filters in spatial and

    fre#uency domains, histogram'

    +' C' .ndrew and B' "' +unt, Digital image restoration, Prentice +all, 78==

    EE621 $ar%o" &'ains and ()e)ing Systems

    Prere#uisite5 Bac!ground in Probability and Stochastic Processes and an interest in Systemodeling';ar!ov Chains and regenerative processes have been extensively used in modeling a wide

    variety of systems and phenomena' &i!ewise, many systems can be modeled as #ueueing systems with

    some aspect of the #ueue governed by a random process' bvious examples of such systems occur in

    telecommunication systems, manufacturing systems and computer systems' )his course is aimed atteaching system modeling using ar!ov chains with special emphasis on developing #ueueing models'

    )he course contents are as follows';*ntroduction5 "eview of basic probability, properties of nonnegativerandom variables, laws of large numbers and the Central &imit )heorem';"enewal Processes5 Basicdefinitions, recurrence times, rewards and renewal reward theorem, point processes, Poisson process,

    alds e#uation, Blac!well/s theorem';Discrete time ar!ov chains5 definitions and properties, matrix

    representation, Perron

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    Stochastic odeling and the )heory ueues, Prentice +all, Cliffs, 7898'

    P'Bremaud, ar!ov Chains, Springer'

    &'4leinroc!, ueueing SystemsG vols * and **, John iley and Sons 78=>'

    EE635 A!!lied *inear Algebra in Electrical Engineering

    1ector spaces, linear dependence, basis; "epresentation of linear transformations with respect to a

    basis';*nner product spaces, +ilbert spaces, linear functions; "ies? representation theorem and

    adAoints';rthogonal proAections, products of proAections, orthogonal direct sums; 0nitary and orthogonal

    transformations, complete orthonormal sets and Parseval/s identity; Closed subspaces and the proAection

    theorem for +ilbert spaces';Polynomials5 )he algebra of polynomials, matrix polynomials, annihilatingpolynomials and invariant subspaces, forms';.pplications5 Complementary orthogonal spaces in networ!s,

    properties of graphs and their relation to vector space properties of their matrix representations; Solution ofstate e#uations in linear system theory; "elation between the rational and Jordan forms';Fumerical linear

    algebra5 Direct and iterative methods of solutions of linear e#uations; atrices, norms, complete metric

    spaces and complete normal linear spaces $Banach spaces%; &east s#uares problems $constrained andunconstrained%; (igenvalue problem'

    Text/References

    4' +offman and "' 4un?e, &inear .lgebra, Prentice%'

    3'+' 3olub and C'2' 1an &oan, atrix Computations, .cademic, 789:'

    3' Bachman and &' Farici, 2unctional .nalysis, .cademic Press, 78>>'

    ('4reys?ig, ntroductory functional analysis with applications John iley, 78=9'

    EE636 $atrix &om!)tations

    Basic iterative methods for solutions of linear systems and their rates of convergence' 3enerali?edconAugate gradient, 4rylov space and &anc?os methods' *terative methods for symmetric, non

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    *ntroduction to linear least s#uare estimation 5 a geometric approach'iener filter, &evinson filter, updating "

    filter and the 4alman filter'2ilter implementation structures 5 lattice, ladder and the systolic "'Stochasticreali?ation theory $modelling given the covariance%' odelling given the raw data' Spectral

    estimation';"ecursive least s#uares identification algorithms5 &evinson

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    C' 4' Chui, .n *ntroduction to avelets, .cademic Press *nc', Few Ior!, 7886'

    3erald 4aiser, . 2riendly 3uide to avelets, Bir!hauser, Few Ior!, 788'

    P' P' 1aidyanathan, ultirate Systems and 2ilter Ban!s, Prentice +all, Few Jersey, 788:'

    .'F' .!ansu and "'.' +addad, ultiresolution signal Decomposition5 )ransforms,

    Subbands and avelets, .cademic Press, ranld, 2lorida, 7886'

    B'Boashash, )ime'

    D' arr, 1ision, 2reeman and Co', San 2rancisco, 7896'

    S' Chaudhuri and .' F' "aAagopalan, Depth from Defocused *mages, Springer 1erlag, FI,

    7888'Selected Papers'

    EE10 *arge S!arse $atrix &om!)tations

    Sparse atrices, applications in electrical engineering, data structures, linear system solvers,

    ordering5 ar!owit? criterion, minimum degree E minimum deficiency ordering for sparsesymmetric positive definite matrices, enhancements to D., sparse indefinite linear system

    solvers, eigen value computation, sparse matrix optimi?ation, applications in power systems5 state

    estimation, load flow E optimal power flow'

    EE+ Ad"anced To!ics in Signal Processing

    *ntroduction < "elevant concepts in DSP, linear algebra, matrix analysis, and statistical signal

    analysis $as needed% Spectral estimation $temporal% < Fon

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    topics in sampling and reconstruction < Dithered sampling, use of a random dither < Sampling,

    #uanti?ation, and interpolation < Sampling of non

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    *. +namic Image +ata ompression in Spatial and Temporal +omain, April .

    /. $orphological Image Enhancement, April .

    . A#tomatic Segmentation of "rain $RI, April .

    0. Image Segmentation E$ Algorithm Initialised Tree Str#ct#re Scheme, April .

    . $ar%ov Random &ield Segmentation of "rain $RI, April .

    '. 1ossless Image compression #sing +T and resid#als, April /.

    . Image segmentation #sing f#33 c-means cl#stering algorithm, April *.

    /. Image data compression #sing dadic transform, April .

    . Edge +etection in an Image 4sing the Rec#rsive 5avelet Transform, April '.

    20. Acc#rate Image Rotation, April 6.