MODULE 1

Introduction to Signals and Systems (9 hours):

Classification of signals: Elementary signals- Basic operations on continuous time and discrete time signals

Concept of system: Classification of systems- Properties of systems- Time invariance- Linearity -Causality – Memory- Stability-Convolution Integral- Impulse response Representation of LTI systems: Differential equation representations of LTI systems Basics of Non linear systems- types and properties

Introduction to random signals and processes (concepts only)

MODULE 2

Fourier Analysis and Laplace Transform Analysis (10 hours):

Fourier analysis of continuous time signals: Fourier Series- Harmonic analysis of common signals

Fourier transform: Existence- Properties of Continuous time Fourier transform- Energy spectral density and power spectral density

Concept of Frequency response

Laplace transform analysis of system transfer function: Relation between the transfer function and differential equation- Transfer function of LTI systems- Electrical, translational and rotational mechanical systems- Force voltage, Force current and Torque Voltage analogy

MODULE 3

System Models and Response (8 hours):

Block diagram representation - block diagram reduction Signal flow graph - Mason's gain formula

Type and Order of the systems- Characteristic equation

Determining the time domain and frequency response from poles and zeros

Concepts of Positive real functions and Hurwitz polynomial- Routh stability criterion. Simulation based analysis: Introduction to simulation tools like MATLAB/ SCILAB or equivalent for mathematical and signal operations (Demo/Assignment only)

MODULE 4

Sampled Data Systems and Z-Transform (9 hours):

Sampling process-Impulse train sampling-sampling theorem- Aliasing effect Zero order and First order hold circuits- Signal reconstruction

Discrete convolution and its properties

Z Transform: Region of convergence- Properties of Z Transform Inverse ZT: Methods

MODULE 5

Analysis of Sampled Data Systems (9 hours):

Difference equation representations of LTI systems - Analysis of difference equation of LTI systems- Z Transfer function- Delay operator and block diagram representation- Direct form, cascade and parallel representations of 2nd order systems

Stability of sampled data system: Basic idea on stability- Jury's test- Use of bilinear transformation

Discrete Fourier series: Fourier representation of discrete time signals - Discrete Fourier series– properties.

Discrete Time Fourier Transform: Properties- Frequency response of simple DT systems