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)

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

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)

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