## Course Detail

 Course Name Mathematics of Signal Processing Course Code 19EAC205 Program B. Tech. in Electronics and Computer Engineering Semester 3 Year Taught 2019

### Syllabus

##### 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.

### Objectives and Outcomes

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

 PO/PSO/ CO PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 CO1 3 2 2 2 CO2 3 2 CO3 3 3 2 CO4 3 3 CO5 2 2

### Textbook / References

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)

 Assessment Internal External Periodical 1 (P1) 15 – Periodical 2 (P2) 15 – *Continuous Assessment (CA) 20 – End Semester – 50 *CA – Can be Quizzes, Assignment, Projects, and Reports.

DISCLAIMER: The appearance of external links on this web site does not constitute endorsement by the School of Biotechnology/Amrita Vishwa Vidyapeetham or the information, products or services contained therein. For other than authorized activities, the Amrita Vishwa Vidyapeetham does not exercise any editorial control over the information you may find at these locations. These links are provided consistent with the stated purpose of this web site.