Probability distributions: random variables (discrete & continuous), probability density,mathematical expectation, mean and variance of a probability distribution, binomial distribution, Poisson approximation to the binomial distribution, uniform distribution ,normal distribution. Curve fitting: method of least squares, correlation and regression,lines of regression.
Sampling distributions: population and samples, the sampling distribution of the mean unknown),σ known), the sampling distribution of the mean (σ( the sampling distribution of the variance, point estimation, interval estimation, tests of hypotheses, nul hypothese and significance tests, hypothesis concerning one mean, type I and type II errors,hypotheses concerning two means. The estimation of variances : Hypotheses concerning one variance - Hypotheses concerning two variances.
Finite difference Operators: ∇, , Ε, δ, μ , x(n) .Newton’s Forward and Backward differences interpolation polynomials, central differences, Stirlings central differences interpolation polynomial. Lagrange interpolation polynomial, divided differences,Newton’s divided differences interpolation polynomial. Numerical differentiation:Formulae fo derivatives in the case of equally spaced points. Numerical integration:Trapezoidal and Simpson’s rules, compounded rules, errors of interpolation and integration formulae. Gauss quadrature formulae (No derivation fo 2 point and 3 point formulae)
Numerical solution of ordinary differential equations: Taylor series method, Euler’s method, modified Euler’s method, Runge-Kutta formulae 4th order formula. Numerical solution of boundary value problems: Methods of finite differences, finite differences methods fo solving Laplace’s equation ii a rectangular region, finite differencesmethods fo solving the wave equation and heat equation.
1. Irvrin Miller & Freind : Probability And Statistics For Engineers, Prentice Hall OfIndia 2. S.S.Sastry: Numerical Methods, PHI Publishers.
1. P.Kandaswamy K.Thilagavathy, K.Gunavathy: Numerical Mehtods, S.Chand & Co.2. A.Papoulis: Probability,Random Variables And Stochastic Processes,MGH Publishers
Vector Analysis : Vector Algebra, Coordinate Systems and Transformation – Cartesian, Cylindrical and spherical coordinates, Vector Calculus – Differential length, area and volume, Line, surface and volume integrals, Del operator, Gradient of a scalar, Divergence of a vector, Divergence Theorem, Curl of a vector, Stoke’s Theorem, Laplacian of a scalar.
Electrostatics: Electrostatic Fields – Coulomb’s Law and field intensity, Electric fields due to continuous charge distributions, Electric flux density, Gauss’s Law, Applications of Gauss’s Law, Electric Potential, Relationship between E and V, Electric dipole, Energy density in Electrostatic fields.Electric fields in material space – Properties of materials, Convection and conduction currents, Conductors, Polarization in Dielectrics, Dielectric constant and strength, Continuity equation, relaxation time, Boundary conditions; Electrostatic Boundary value problems–Poisson’s and Laplace’s Equations, Uniqueness Theorem, Resistance and capacitance [Parallel-plate, coaxial, spherical capacitors].
Magnetostatics and Maxwell’s equations: Magnetostatic fields – Biot-Savart’s Law, Ampere’s circuital law, Applications of Ampere’s circuital law, Magnetic flux density, Magnetic scalar and vector potentials. Magnetic forces, Materials and devices – Forces due to magnetic fields, Magnetic torque and moment, Magnetic dipole, Magnetization in materials, Classification of Magnetic Materials, Magnetic boundary conditions, Inductors and inductances, Magnetic energy, Magnetic circuits. Faraday’s Law, Displacement current, Time-harmonic fields, Maxwell’s equations for static fields and time varying fields.
Electromagnetic wave propagation : Electromagnetic waves-Wave propagation in lossy dielectrics- Wave equations, propagation constant, intrinsic impedance of the medium, complex permittivity, loss tangent, Plane waves in lossless dielectrics, Plane waves in free space – uniform plane wave, Plane waves in good conductors – skin effect, Poynting vector, Poynting’s Theorem, Reflection of a plane wave at normal incidence – standing waves, Reflection of a plane wave at oblique incidence – parallel and perpendicular polarization, Brewster angle.
Overview of Embedded System: - Embedded System, Categories of Embedded System, Requirements of Embedded Systems, Challenges and Issues in Embedded Software Development, major application areas of embedded system. Typical embedded system- Core of the embedded system, memory, sensors and actuators, Communication Interface, reset circuit, Brown-out protection circuit, oscillator circuit, Watchdog timer .Overview of the 8051 family. 8051 architecture- memory organization, registers and I/O ports. Addressing modes, instruction sets, and assembly language programming. Programming timer/counter. Interrupts- handling and programming. Introduction to C programming in 8051.
8051 interfacing - keyboard, stepper motor, ADC, DAC, and LCD module interface. Applications - frequency counter and temperature measurement. Bus architectures & protocol of I2C, SPI, CAN, RS232.
Memory-Technology & devices -Flash memory-NAND Flash -NOR Flash-DRAM-SDRAM/ DDR/ DDR2. Introduction to embedded CPUs: Basic architecture of ARM core family-features of ARM 926EJS core. Basic architecture of MSP430-features of MSP430.
Introduction to embedded firmware & operating systems: Boot loader -Realtime kernel-Embedded OS- Tasks, Processes and Threads, Multiprocessing and Multitasking, Task scheduling, Task communication and synchronisation, Device Drivers.
Introduction: Digital communication system, Complex baseband representation of signals, Gram-Schmidt orthogonalisation procedure. M-ary orthogonal signals. Modulation: Carrier modulation (M-ary ASK, PSK, FSK, DPSK), Continuous phase modulation (QPSK and variants, MSK, GMSK). Band width required – Generation.
Receiver: Coherent and non-coherent demodulation: Matched filter, Correlator demodulator, square-law, and envelope detection Detector, Optimum rule for ML and MAP detection Performance: Bit-error-rate, symbol error rate for coherent and non coherent schemes. Probability of error of binary DPSK – Performance of M-ary signaling schemes in AWGN channels.
Base band data transmission Line codes-NRZ, RZ, Phase encoded, Multilevel binary. Band-limited channels: Pulse shape design for channels with ISI: Nyquist pulse, Partial response signaling, Channel with distortion: Zero forcing Equalizer- Decision Feedback Equalizer-Preset and Adaptive Equalizer- Scrambling and descrambling. Different synchronization techniques -Early-Late Gate, MMSE, ML and spectral line methods, Carrier, symbol timing.
Fundamental concepts of spread spectrum systems-pseudo noise sequence-performance of direct sequence spread spectrum systems-analysis of direct Sequence spread spectrum systems- the prosing gain and anti jamming margin-frequency hopped spread spectrum systems –time hopped spread spectrum systems-time synchronization.
Introduction to operational amplifiers Op-amp parameters - ideal op amp Frequency response, frequency compensation. Slew rate and its effect; Input bias current –offset - drift - compensating networks CMRR, SVRR, finite gain bandwidth and its effect in opamp circuits’ performance.Open loop configurations Op amp in closed loop configuration: Different feed back configurations- Voltage series feedback and voltage shunt feedback - concept of virtual ground- linear circuits: Summer- Subtractor, Integrator and differentiator voltage follower - V/I converters, I/V converters and its applications - Differential amplifiers with one op amp and 3 op amps- Use of offset minimizing resistor (ROM) and its design. Instrumentation amplifier IC and its application
Op amp applications- Log amplifier- Antilog amplifier- Comparators: zero crossing- using voltage reference- regenerative (Schmitt trigger) comparators, window detector application – OPAMP as comparators - Astable and monostable multivibrators- Triangular and saw tooth wave generators- - RC phase shift and Wien bridge oscillators-Sample and hold circuit- Peak detector circuit. Precision rectifiers.
Filters: Transfer functions - LPF, HPF, BPF, BRF Approximation methods - Butter worth - Chebyshev -Active Filters - I order and II order filters, Quality factor-Design – Gyrator - Negative Impendence Converter - Filter using Simulated Inductance - Universal Active Filters - All Pass filters. Switched Capacitive Filters. ADC and DAC - performance specification - weighted, R-2R, successive approximation, flash, integrating.
Specialized ICs and applications: Voltage regulator IC 723, current limiting, short circuit protection, Thermal protection -555 timers – Functional block diagram- AstableMultivibrator, MonostableMultivibrator and its applications.- 566 VCO chip- Phase locked loop (PLL) - block diagram, Mathematical Derivation of capture range, lock range and pull in time capture and lock range- 565 PLL - PLL applications: Frequency multiplication and division- AM demodulation - FM detection - FSK demodulation Analog multiplier circuits and applications.
Discrete Time Fourier Transform (DTFT) – Properties - Discrete Fourier Transform (DFT) – Properties – circular convolution – Linear convolution – Efficient computation of DFT : Fast Fourier Transform (FFT) – Decimation in Time (DIT) – Decimation in Frequency (DIF) – practical considerations - Discrete Hilbert transforms - Introduction to Discrete Hilbert Transforms, DCT, STFT, Wavelet Transform.
Finite Impulse Response (FIR) Filters – Basic structures – direct, cascade, linear phase, frequency sampling and lattice - Design of FIR filters – Fourier series truncation – Windowing: Rectangular, Bartlett - Blackman – Hanning - Hamming – Frequency Sampling – Finite register length effects - Application of FIR filters.
Infinite Impulse Response (IIR) Filters – Basic structures : Direct form I & II , cascade and Parallel – Design of IIR Filters – Butterworth – Chebyshev - Impulse Invariance – Bilinear Transformation – Frequency transformations – Finite register Length effects – Applications of IIR Filters – Dual Tone multi frequency generation and detection.
General and Special purpose Digital Signal Processors –Harvard architecture – Pipelining – Hardware Multiplier Accumulator -Special Instructions - Fixed and Floating Point Processors – TMS320C54X –Architecture – Instruction set - Addressing modes –- TMS320C67X – Architecture - Instruction set Addressing modes .