NATIONAL INSTITUTE OF TECHNOLOGY MEGHALAYA _____________________________________________________________________ _ ELECTRONIC AND COMMUNICATIONS ENGINEERING DEPARTMENT Syllabus for Written Test to Ph. D Programme, August 2015. Group A: (30 Marks: MCQ) 1) Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson,Normal and Binomial distributions. 2) Discrete Mathematics: Basic operations on sets, cartesian products, disjoint union (sum), andpower sets. Different types of relations, their compositions and inverses. Different types of functions, their compositions and inverses. Complete partial ordering, chain, lattice. complete, distributive, modular, andcomplemented lattices. Boolean and pseudo boolean lattices.Algebraic structures with one binary operation – semigroup, monoid and group.Cosets, Lagrange’s theorem, normal subgroup, homomorphic subgroup.Congruence relation and quotient structures.Error correcting code.Algebric structures with two binary operations- ring, integral domain, and field. Boolean algebra and boolean ring. 3) Logical Reasoning, Data Analysis & Interpretation and Verbal Ability: Number Sequence Completion, Pattern Completion, Sets based on grouping and patterns, Seating Arrangement problems, Circular Arrangements, Relational problems, Selection and Conditionals, Mapping and best routes, Miscellaneous sets consisting of formal logic, testing, sports events and other critical reasoning, Data Analysis, Data Interpretation, Data Sufficiency, Reading Comprehension, Verbal Logic, Vocabulary, Grammar Correction. Group B: (40 Marks: MCQ) This section will cover fundamentals from B. Tech Syllabus in Electronic and Communications Engineering. Group C: (30 Marks: Descriptive) Candidate is required to answer one of the groups. However, his/her selection may not be limited to that specialization only. 1. Detailed Syllabus for VLSI Signal Processing Signal Processing: Review of LTI systems and their properties, Convolution sum, Sampling of continuous time signals, Discrete-time Fourier transform (DTFT) and its properties, Sampling in frequency NATIONAL INSTITUTE OF TECHNOLOGY MEGHALAYA _____________________________________________________________________ _ domain, Discrete Fourier transform (DFT) and its properties, Z-transform, stability analysis, implementation of discrete-time systems, design of FIR filters and IIR filters, linear phase filters, group delay, response of first and second order filters, Applications of DSP. VLSI Design systems: I. Basic of Digital Design: Introduction to digital system, Basic combinational circuits like adders, Multiplexers, encoder, decoders, various Flip-Flops, counters, shift registers, Memory, Synchronous and Asynchronous system design, , Finite State Machine with case studies . Design flow for ASIC and FPGA Design, Introduction to RTL (HDL) coding. II. MOSFET operation and V-I characteristics, CMOS Inverters Analysis and Design, Switching Properties of MOSFET, CMOS Static logic gates, CMOS Combinational and Sequential logic Circuits, Transmission gate logic circuits, CMOS Dynamic logic Families, Semiconductor Memories. III. Introduction to computers, number representation, fixed point arithmetic, ALU organization, floating point arithmetic, FPU, Decimal (BCD) arithmetic, Instruction formats and addressing modes, Hardwired and Micro-programmed control units, Memories and memory interfacing, System buses, Peripheral interfaces, I/O modes: Programmed, Interrupt, DMA, I/O processor, Basic CPU design,, Advances in computer architecture, super scalar processors, Virtual memory concept, Multi-programming and multi tasking, RISC vs. CISC 2. Detailed Syllabus for Computer Arithmetic Number Representation: Numbers and Arithmetic: What is computer arithmetic?, Motivating Examples, Numbers and their encodings, Fixed- radix positional number systems, Number radix conversion, Classes of number representations. Representing Signed Numbers: Signed-magnitude representation, Biased representations, Complement representations, Two'sand 1's-complement numbers, Direct and indirect signed arithmetic, Using signed positions or signed digits. Redundant Number Systems: Coping with the carry problem, Redundancy in computer arithmetic, Digit sets and digit-set conversions, Generalized signed-digit numbers, Carry-free addition algorithms, Conversions and support functions. Introduction to Residue Number systems. Addition / Subtraction: Basic Addition and Counting: Bit-serial and ripple-carry adders, Conditions and exceptions, Analysis of carry propagation, Carry completion detection, Addition of a constant: counters, Manchester carry chains and adders. Carry-Look Ahead Adders: Unrolling the carry recurrence, Carry-lookahead adder design, Ling adder and related designs, Carry determination as prefix computation, Alternative parallel prefix networks, VLSI implementation aspects Variations in fast adders: Simple carry-skip adders Multilevel carry- NATIONAL INSTITUTE OF TECHNOLOGY MEGHALAYA _____________________________________________________________________ _ skip adders, Carry-select adders, Conditional-sum adder, Hybrid designs and optimizations, Modular two-operand adders Multiplication: Basic Multiplication Schemes: Shift/add multiplication algorithms, Programmed multiplication, Basic hardware multipliers, Multiplication of signed numbers, Multiplication by constants, Preview of fast multipliers. High-Radix Multipliers: Radix-4 multiplication, Modified Booth's recoding, Using carry-save adders, Radix-8 and radix-16 multipliers, Multibeat multipliers, VLSI complexity issues. Tree and Array Multipliers: Full-tree multipliers, Alternative reduction trees, Tree multipliers for signed numbers, Partialtree and truncated multipliers, Array multipliers, Pipelined tree and array multipliers. Division: Basic Division Schemes: Shift/subtract division algorithms, Programmed division, Restoring hardware dividers, Nonrestoring and signed division, Division by constants, Radix-2 SRT division. High-Radix Dividers: Basics of high-radix division, Using carry-save adders, Radix-4 SRT division, General highradix dividers, Quotient- digit selection, Using p-d plots in practice. Variations in Dividers: Division with prescaling , Overlapped quotient-digit selection, Combinational and array dividers, Modular dividers and reducers, The special case of reciprocation, Combined multiply/divide units. Real Arithmetic: Floating-Point Representations, Floating-point numbers, The ANSI/IEEE floating-point standard, Basic floating-point algorithms, Conversions and exceptions, Rounding schemes, Logarithmic number systems. Floating-Point Operations: Floating-point adders/subtractors, Pre- and postshifting, Rounding and exceptions, Floatingpoint multipliers and dividers, Fused-multiply-add units, Logarithmic arithmetic unit. 3. Detailed Syllabus for Wireless Communication Fundamentals of information theory and channel capacity theorem. Characteristics of wireless channel and propagation path loss models: Different Multi-path propagation mechanisms, Multi-path effects on mobile communication, Fading, different types of fading, small and large scale fading, slow and fast fading, narrowband and wideband fading, Inter symbol interference, fast fading model, Doppler effect due to velocity of mobiles, Rayleigh envelop, free space propagation model, log normal shadowing model, macro and micro cell propagation model. NATIONAL INSTITUTE OF TECHNOLOGY MEGHALAYA _____________________________________________________________________ _ 4. Detailed Syllabus for Antenna Array Design Antenna Characteristics: Radiation Pattern, Beam Width; Radiation Resistance and efficiency; Directivity and Gain; Impedance, VSWR, Polarization; Effective height and Receive Aperture; Noise Temperature of Antenna. Antenna Arrays: electric Field due to 2 element arrays, 3 element Arrays; Pattern Multiplication; Uniform Linear Array: End fire and Broad side; Phased array. Characteristics and properties of: Travelling Wave Antenna, Helical Antenna, Folded Dipole, Yagi-Uda Array, Loop Antenna, Electrically Short Antennas, Broad Band Antenna (Log periodic Antenna), Microstrip Patch Antenna. Methods of Propagation: Ground Wave Propagation, Components of ground wave, Field strength dependence on physical factors. Sky wave Propagation; Ionospheric Layers; Virtual Height, Critical Frequency, MUF, Skip distance, Sporadic Reflections. Space wave propagation: Tropospheric Scatter, Ducting Super refraction. 5. Detailed Syllabus for Wireless Sensor Networks Same as Syllabus for Wireless Communication 6. Detailed Syllabus for Communications and Signal Processing: Basic signals and systems concepts, Linear time-invariant systems, Transform analysis of linear time-invariant systems, Fourier analysis for continuous-time signals and systems, Sampling of continuous time signals, Discrete-time signals and systems, Fourier analysis for discrete-time signals and systems, Laplace transform, Z transform and Discrete Fourier transform. Probability and random variables: The meaning of probability, the axioms of probability, repeated trials, the concept of a random variable, functions of one random variable and two random variables. Baseband digital transmission, Information theory, Source and channel coding, Bandpass digital transmission. **********************************

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