Module I

Introduction: Signals: Classification of signals, Continuous – Discrete time; Even/Odd signals, Periodic/ Nonperiodic signals, Deterministic/Random signals, Energy/Power signals; Basic operations on signals: Basic (Continuous/Discrete) signals – unit step, unit impulse, sinusoidal and complex exponential signals etc. Systems (Continuous/Discrete): Representation, Classification – Linear/Nonlinear, Causal/Non-causal, Time invariant/Time variant, with/ without memory; BIBO stability, Feedback system. LTI system – Response of LTI system, Convolution, Properties (Continuous/Discrete); LTI systems – Differential/Difference equation representation and solution.

Module II

Fourier series: Fourier series – half range expansions –Parseval’s identity – Transform integrals –Fourier Integrals – theorem – Sine and cosine integrals. Fourier analysis of continuous time signals and systems: Fourier series for periodic signals; Fourier transform – Properties of continuous time FT. Sampling: Sampling theorem, Reconstruction of signal, Aliasing, Sampling of discrete time signals; Introduction to DFT and its properties.

Module III

Laplace transform analysis of systems – Inverse transforms, linearity, shifting, Transforms of derivatives and integrals – ROC – Frequency response of continuous time LTI systems. Z transforms – definition – ROC – inverse transforms – properties, frequency response of discrete time LTI systems. Inter-relationship between different representations and transforms.

Course Objectives

• To introduces the basic principles of signals and system analysis.
• To cover various basic tools of signal and system analysis such as signal classification, LTI systems and its properties, Convolution, Frequency Response, Laplace transform, Z transform and Fourier analysis.
• To make the students understand and analyze various important concepts such as convolution, impulse/ frequency response, causality, stability of systems will be especially emphasized.

Course Outcomes

• CO1: Ability to represent the basic continuous time and discrete time signals and systems.
• CO2: Ability to understand the spectral characteristics of continuous / discrete-time periodic and aperiodic signals using Fourier analysis.
• CO3: Ability to analyze system properties based on impulse response and Fourier analysis.
• CO4: Ability to analyze and characterize LTI system using transforms.

CO – PO Mapping

Textbook / Reference

• Simon Haykin, Barry Van Veen, “Signals and Systems”, Second Edition, John Wiley and Sons, 2005.
• Alan V. Oppenheim, Alan S. Willsky ,S, Hamid Nawab, “Signals and Systems”, Prentice Hall India Private Limited, 1997.
• Michael. J. Roberts, “Fundamentals of Signals and Systems”, First Edition, Tata McGraw Hill Publishing Company Limited, 2007.
• Rodger E. Ziemer, William. H. Tranter, D. Ronald Fannin, “Signals and Systems”, Fourth Edition, Pearson Education, 2004.

Evaluation Pattern 50:50 (Internal: External)