# NIT Srinagar Syllabus

### Signals & Systems

Introduction to signals: Classification of signals; Deterministic and non-deterministic, periodic and aperiodic, even and odd signals, energy and power signals, elementary signals; exponential, sinusoidal, impulse, step, ramp, pulse, square wave signals. Time shifting, time scaling and time-inversions of signals.

Linear Time invariant systems: Continuous time system, basic system properties like causality, time invariance, stability, linearity, memory, order of system, interconnection of systems, Linear time invariant systems, characterization, unit impulse response , convolution, properties of LTI systems, linear constant co-efficient differential equations and system description.

Fourier analysis of signals and systems: Fourier series of periodic signals and its properties, Fourier transform of aperiodic signals and its properties, fourier transform of periodic signals, convolution in time and frequency domain, energy and signals, parsevals theorem, energy spectral density and its properties, Transfer function of LTI system

The Laplace Transform: Definition, relation between Laplace and Fourier transforms, region of convergence, properties of Laplace transform, initial and final value theorems, convolution, transfer function of LTI system, concept of poles and zeroes, stability criteria

Random variable theory and random signals: Probability, conditional probability, statistical independence, random variables, discrete and continuous random variables, probability distribution and probability density functions, statistical averages of random variables. Some important density functions.

Random processes and characterization: Ensemble and time averages, stationary and non-stationary random process, wide sense stationery random process, autocorrelation and cross-correlation functions, response of LTI systems to random inputs, noise and its types, white noise, signal to noise ratio of LTI systems.

#### Books Recommended:

1. Signals and Systems by Zieman, Tranter, Fannin.
2. Signals and Systems by Sanjay Sharma.
3. Signals and Systems by A Populis.
4. Random processes and Systems by A Populis.
5. Signals and Systems by S. Hykin.