28-06-2012, 11:38 AM
MATHEMATICAL METHODS FOR ELECTRONICS
[attachment=25875]
Algebraic structures. Sets-relations-Groups-subgroups-cosets and Lagranges Theorem
Rings Integral domain and Fields-Definition and examples.
Linear Algebra. Vector space-subspace-linear dependence-basis-dimension-Interpolation and wronskian-Linear Transformation-change of bases-diagonalization.
Eigen values and eigen vectors-diagonalization of matrices--exponential matrices-of linear recurrence relations.
Probability spaces: Random variables-distributions and densities-statistical independence-expectations-moments and characteristic functions.
Sequence of random variables and it’s convergence-Chebychev’s inequality-law of large numbers-Central limit theorem.
Random processes: Definition and classification of random processes-stationarity(strict sense and wide sense)-Autocorrelation function and its properties.-Ergodicity- ergodic theorems. spectral density function and it’s properties.
Special Random Processes.Poisson process-properties-Markov process- Markov Chains-Transition probability matrix-Chapman-Kolmogorov theorem.-Birth death process-weiner process.
ADVANCED DIGITAL SIGNAL PROCESSING
Basics of Multirate systems and its application, up sampling and Down - Sampling, Fractional Sampling rate converter. Polyphase decomposition. Efficient realisation of Multirate systems.Uniform filter banks and it's implementation using polyphase decomposition. Two channel Quadrature Mirror Filter Banks, Perfect Reconstruction, M-channel PR QMFB.
Time Frequency Analysis, Heisenberg's uncertinity principle. Short time fourier transform - Gabor transform. Continous Wavelet Tranform and it's properties. Multi Resolution Analysis, Discrete Wavelet Transform, Orthonormal Wavelet Analysis - Filterbank interpertation. Haar and Daubechise wavelets, Bi-orthogonal wavelets and Filter bank interpretation. B -Spline wavelets, Wavelet packets.2D wavelt transforms. Application of wavelet tranform for data compression, noise reduction.
Linear Prediction -Forward and Backward Prediction - Levinson-Durbin Algorithm, Schur Algorithm.
Power spectrum estimation of signals: Wide Sense Stationary Random Processes. Power spectral density. Non parametric methods: periodogram,Backman-Tuckey method. Parametric method: ARMA, AR processes, Yule-Walker method.
NON-LINEAR CONTROL SYSTEM
Non-linear systems
-Characteristics, Common non linearities.
Method of Analysis:
-Linearization techniques
-Describing function analysis of non-linear systems. Dual input Describing
function.(DIDF)
-Phase plane analysis of non-linear systems, existence of limit cycles
- Lyapunov stability theory for continuous and discrete time systems.
Construction of Lyapunov function.
Non linear control system design:
-Variable structure controller and sliding control.
- Implementation of switching control laws.
- Cascade design.
-Partial state feedback design.
ADAPTIVE CONTROL SYSTEMS
Different adaptive control strategies - Gain scheduling, MRAS, STR, stochastic adaptive control - Lp spaces - Norms, - stability of Dynamic system. Differential equations, stability definitions - Lyapunov stability Theory - Exponential stability theorems – estimating parameters in dynamic systems with least square methods .
MRAS – adaptation law – adaptation law based on stability criterion – adaptation based on MIT rule – Design of MRAS based on MIT rule – Design of MRAS based on Lyapunov methods – simulation of MRAS systems.
Self Tuning Regulators – Pole placement design – Indirect STR – continuous time STR –Direct STR- simulation of STR systems - stochastic self tuning regulators- linear quadrant STR – adaptive predictive control .
[attachment=25875]
Algebraic structures. Sets-relations-Groups-subgroups-cosets and Lagranges Theorem
Rings Integral domain and Fields-Definition and examples.
Linear Algebra. Vector space-subspace-linear dependence-basis-dimension-Interpolation and wronskian-Linear Transformation-change of bases-diagonalization.
Eigen values and eigen vectors-diagonalization of matrices--exponential matrices-of linear recurrence relations.
Probability spaces: Random variables-distributions and densities-statistical independence-expectations-moments and characteristic functions.
Sequence of random variables and it’s convergence-Chebychev’s inequality-law of large numbers-Central limit theorem.
Random processes: Definition and classification of random processes-stationarity(strict sense and wide sense)-Autocorrelation function and its properties.-Ergodicity- ergodic theorems. spectral density function and it’s properties.
Special Random Processes.Poisson process-properties-Markov process- Markov Chains-Transition probability matrix-Chapman-Kolmogorov theorem.-Birth death process-weiner process.
ADVANCED DIGITAL SIGNAL PROCESSING
Basics of Multirate systems and its application, up sampling and Down - Sampling, Fractional Sampling rate converter. Polyphase decomposition. Efficient realisation of Multirate systems.Uniform filter banks and it's implementation using polyphase decomposition. Two channel Quadrature Mirror Filter Banks, Perfect Reconstruction, M-channel PR QMFB.
Time Frequency Analysis, Heisenberg's uncertinity principle. Short time fourier transform - Gabor transform. Continous Wavelet Tranform and it's properties. Multi Resolution Analysis, Discrete Wavelet Transform, Orthonormal Wavelet Analysis - Filterbank interpertation. Haar and Daubechise wavelets, Bi-orthogonal wavelets and Filter bank interpretation. B -Spline wavelets, Wavelet packets.2D wavelt transforms. Application of wavelet tranform for data compression, noise reduction.
Linear Prediction -Forward and Backward Prediction - Levinson-Durbin Algorithm, Schur Algorithm.
Power spectrum estimation of signals: Wide Sense Stationary Random Processes. Power spectral density. Non parametric methods: periodogram,Backman-Tuckey method. Parametric method: ARMA, AR processes, Yule-Walker method.
NON-LINEAR CONTROL SYSTEM
Non-linear systems
-Characteristics, Common non linearities.
Method of Analysis:
-Linearization techniques
-Describing function analysis of non-linear systems. Dual input Describing
function.(DIDF)
-Phase plane analysis of non-linear systems, existence of limit cycles
- Lyapunov stability theory for continuous and discrete time systems.
Construction of Lyapunov function.
Non linear control system design:
-Variable structure controller and sliding control.
- Implementation of switching control laws.
- Cascade design.
-Partial state feedback design.
ADAPTIVE CONTROL SYSTEMS
Different adaptive control strategies - Gain scheduling, MRAS, STR, stochastic adaptive control - Lp spaces - Norms, - stability of Dynamic system. Differential equations, stability definitions - Lyapunov stability Theory - Exponential stability theorems – estimating parameters in dynamic systems with least square methods .
MRAS – adaptation law – adaptation law based on stability criterion – adaptation based on MIT rule – Design of MRAS based on MIT rule – Design of MRAS based on Lyapunov methods – simulation of MRAS systems.
Self Tuning Regulators – Pole placement design – Indirect STR – continuous time STR –Direct STR- simulation of STR systems - stochastic self tuning regulators- linear quadrant STR – adaptive predictive control .