What You will Learn ?

Module 1: Introduction to Signals and Systems

Classification of signals: Elementary signals, basic operations on continuous and discrete time signals. Concept of system: Classification of systems, properties of systems such as time invariance, linearity, causality, memory, and stability. Convolution integral and impulse response. Representation of LTI systems: Differential equation representations of LTI systems. Basics of nonlinear systems: Types and properties. Introduction to random signals and processes (concepts only).

Module 2: Fourier Analysis and Laplace Transform Analysis

Fourier analysis of continuous time signals: Fourier Series and 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, and applications in electrical, translational, and rotational mechanical systems. Force-voltage, force-current, and torque-voltage analogies.

Module 3: System Models and Response

Block diagram representation and block diagram reduction. Signal flow graph and Mason's gain formula. System type and order, characteristic equation, and determining 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

Sampling process: Impulse train sampling, sampling theorem, and 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

Difference equation representations of LTI systems, analysis of difference equations for LTI systems, Z transfer function, delay operator, and block diagram representation. Direct form, cascade, and parallel representations of second-order systems. Stability of sampled data systems: Basic idea on stability, Jury's test, and bilinear transformation usage. Discrete Fourier Series: Fourier representation of discrete-time signals, discrete Fourier series properties. Discrete Time Fourier Transform: Properties and frequency response of simple discrete-time systems.