Matlab program to plot real, imaginary phase and magnitude of exponential function.

clc;
k = input('Enter the value of gain,k:');
a = input('Enter the value of a,a:');
N = input('Enter the value of N:');
n = 0:1:N;
y = k*(a.^n);
subplot (3,1,1);
stem (n,y);
xlabel ('time');
ylabel ('amplitude');
title ('Exponential Sequence')
p = input('Enter the value of gain,p:');
a1 = input('Enter the value of real part,a1:');
b1 = input('Enter the value of imaginary part,b1:');
N1 = input('Enter the value of N1:');
n1 = 0:1:N1;
c = a1+b1*j;
x = p*(c.^n1);
subplot (3,1,2);
stem (n1,real(x));
xlabel ('time');
ylabel ('amplitude');
title ('Real Exponential Sequence')
subplot (3,1,3);
stem (n1,imag(x));
xlabel ('time');
ylabel ('amplitude');
title ('Complex Exponential Sequence')
disp ('Result is');
disp (x);

Output

Enter the value of gain,k:4
Enter the value of a,a:5
Enter the value of N:7
Enter the value of gain,p:4
Enter the value of real part,a1:5
Enter the value of imaginary part,b1:3
Enter the value of N1:5
Result is
1.0e+004 *
0.0004 0.0020 + 0.0012i 0.0064 + 0.0120i -0.0040 + 0.0792i -0.2576 + 0.3840i -2.4400 + 1.1472i

Gate 2013 syllabus for elctronics and communication engineering (ECE)

 

SYLLABUS FOR ELECTRONICS AND COMMUNICATION ENGINEERING (EC)

Engineering Mathematics 
Linear Algebra:

Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
 

Calculus:

Mean value theorems, Theorems of integral calculus,  Evaluation of definite and
improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier
series. Vector identities, Directional derivatives, Line, Surface and Volume integrals,
Stokes, Gauss and Green's theorems.

Differential equations:

First order equation (linear and nonlinear), Higher order linear differential equations with
constant coefficients, Method of variation of parameters, Cauchy's and Euler's
equations, Initial and boundary value problems, Partial Differential Equations and
variable separable method.
Complex variables:

Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent'
series, Residue theorem, solution integrals.

Probability and Statistics:

Sampling theorems, Conditional probability, Mean, median, mode and standard
deviation, Random variables, Discrete and continuous distributions, Poisson, Normal
and Binomial distribution, Correlation and regression analysis.

Numerical Methods:

Solutions of non-linear algebraic equations, single and multi-step methods for
differential equations.
Transform Theory: Fourier transform, Laplace transform, Z-transform.
Electronics and Communication Engineering

Networks:

Network graphs: matrices associated with graphs; incidence, fundamental cut set and
fundamental circuit matrices. Solution  methods: nodal and mesh analysis. Network
theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta
transformation. Steady state sinusoidal analysis using phasors. Linear constant
coefficient differential equations; time domain analysis of simple RLC circuits, Solution
of network equations using Laplace transform: frequency domain analysis of RLC
circuits. 2-port network parameters: driving point and transfer functions. State equations
for networks.
Electronic Devices: 

Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon:
diffusion current, drift current, mobility, and resistivity. Generation and recombination of
carriers. p-n junction diode, Zener diode,  tunnel diode, BJT,  JFET, MOS capacitor,
MOSFET, LED, p-I-n and avalanche photo  diode, Basics of LASERs. Device
technology: integrated circuits fabrication process, oxidation, diffusion, ion implantation,
photolithography, n-tub, p-tub and twin-tub CMOS process.

Analog Circuits: 

Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple
diode circuits, clipping, clamping, rectifier. Biasing and bias  stability of transistor and
FET amplifiers. Amplifiers: single-and multi-stage, differential and operational, feedback,
and power. Frequency response of amplifiers. Simple op-amp circuits. Filters.
Sinusoidal oscillators; criterion for  oscillation; single-transistor and op-amp
configurations. Function generators and wave-shaping circuits, 555 Timers. Power
supplies.

Digital circuits:

Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL,
TTL, ECL, MOS, CMOS). Combinatorial circuits: arithmetic circuits, code converters,
multiplexers, decoders, PROMs and PLAs. Sequential circuits: latches and flip-flops,
counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor
memories. Microprocessor(8085): architecture, programming, memory and I/O
interfacing.

Signals and Systems:  

Definitions and properties of Laplace transform, continuous-time and discrete-time
Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, ztransform. Sampling theorem. Linear Time-Invariant (LTI) Systems: definitions and
properties; causality, stability, impulse response, convolution, poles and zeros, parallel
and cascade structure, frequency response,  group delay, phase delay. Signal
transmission through LTI systems. 
Control Systems:

Basic control system components; block diagrammatic description, reduction of block
diagrams. Open loop and closed loop (feedback) systems and stability analysis of these
systems. Signal flow graphs and their use in determining transfer functions of systems;
transient and steady state analysis of LTI control systems and frequency response.
Tools and techniques for LTI control system analysis: root loci, Routh-Hurwitz criterion,
Bode and Nyquist plots. Control system  compensators: elements of lead and lag
compensation, elements of Proportional-Integral-Derivative (PID) control. State variable
representation and solution of state equation of LTI control systems.

Communications:

Random signals and noise: probability, random variables, probability density function,
autocorrelation, power spectral density. Analog communication systems: amplitude and
angle modulation and demodulation systems, spectral analysis of these operations,
superheterodyne receivers;  elements of hardware, realizations of analog
communication systems; signal-to-noise ratio (SNR) calculations for amplitude
modulation (AM) and frequency modulation (FM) for low noise conditions.
Fundamentals of information theory and channel capacity theorem. Digital
communication systems: pulse  code modulation (PCM),  differential pulse code
modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift
keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consideration
and probability of error calculations for  these schemes. Basics of TDMA, FDMA and
CDMA and GSM.

Electromagnetics:   

Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems,
Maxwell's equations: differential and integral forms. Wave equation, Poynting vector.
Plane waves: propagation through various media; reflection and refraction; phase and
group velocity; skin depth. Transmission lines: characteristic impedance; impedance
transformation; Smith chart; impedance matching; S parameters, pulse excitation.
Waveguides: modes in rectangular waveguides; boundary conditions; cut-off
frequencies; dispersion relations. Basics of propagation in dielectric waveguide and
optical fibers. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.