IITB ECE Syllabus

Can anyone provide syllabus of Ph.D Entrance Exam conducted by Indian Institute of Technology Bombay (IITB) for ECE Discipline?

I want to inform you that the Indian Institute of Technology Bombay (IITB) offers Ph.D Degree in Electrical Engineering.

There is no Electronics and Telecommunication Engineering (ECE) discipline offering by Indian Institute of Technology Bombay (IITB) for all courses offering there.

Here I am providing syllabus of Ph.D Electrical Engineering Entrance Exam for your reference:

Indian Institute of Technology Bombay (IITB) Ph.D E.E. Entrance Exam Syllabus

PART A:
This part deals with general mathematical ability for Ph.D. level research in Electrical Engineering.Some topics that could be tested are: Principles of Calculus: Maxima/minima, derivative, integral,elementary multivariate calculus. Basic Transform Theory: Laplace and Fourier transforms.Elementary Linear Algebra and Matrix Theory.Basic probability theory.Basic differential equations.

Vector analysis and vector calculus: divergence, gradient, curl. Complex analysis.

Basic Series expansions: Taylor series. In addition, mathematical principles learned at high schooland in the first couple of years in an Undergraduate Degree, could be tested.

PART B:
EE1 Communication and Signal Processing:
Signals and Systems:
Continuous-time and discrete-time signals and systems
LTI systems and representations
Sampling and reconstruction
Transform domain analysis (Fourier, Laplace, and Z-transforms),
Discrete Fourier transforms (DFT)
Basics of filter design

Probability and Random Processes:
Random variables, Expectation Theory, Generating functions,
Cumulative distribution functions (CDFs), Probability density functions(PDFs), conditional CDFs and PDFs, conditional expectation, functions ofone and two random variables
Probability inequalities (e.g., Markov, Chebyshev, Chernoff, Schwartz)
Random vectors, Joint CDFs and PDFs, Joint moments, Joint characteristicfunctions
Laws of large numbers, Central limit theorem
Gaussian processes, Power spectral density
Basics of detection and estimation.

Analog and Digital communication:
Modulation techniques, Signal representation, Quantization,
Power and bandwidth considerations
Noise in communication systems
Entropy and mutual information, Data compression techniques
Probability of error in digital communications

Communication Networks:
ARQ strategies
MAC protocols
Routing algorithms

EE2 (Control and Computing):
Maxima/minima, polynomials, roots, Routh Hurwitz criteria Linear algebra: rank, vector space, basis,solution to Ax=b, eigenvalues, eigenvectors. Transfer functions, impulse/step response, poles/zeros,root-locus,Bode-plots, Gain/phase margins, low-pass/high-pass characteristics, Nyquist plots,Nyquist criterion for stability.

State space systems, controllability/observability: definition and tests, pole-placement using statefeedback,PBH test. Controller synthesis for reduced steady state error, faster transients:
PD, PID, lead, lag compensators.

EE3 (Power Electronics and Power Systems):
Electric machines, power systems, control theory and Power Electronics of senior undergraduatelevel.

EE4 (Microelectronics):
Electrons in solids, Energy band theory, Charge carriers in semiconductors, Drift-diffusion theory, P-njunctions, Field-effect transistors, Bipolar junction transistors, Optoelectronic and photovoltaicdevices, Digital and analog circuits, Digital systems

EE5 (Electronic Systems):
Basic Electric circuits and networks; Analog and Digital Circuits - analysis and synthesis; Electronicinstrumentation - principles and practices; Elements of Signals, Systems and Signal Processing;Digital Signal Processing - principles, algorithms and elementary architectures; Basic computerarchitecture.

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