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Course Detail

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


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

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.

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