Signals & Systems

Curriculum

Course Outcomes:

Upon completion of this course the student will be able to:

  • CO1: Apply Linear Algebra techniques for Signal processing

  • CO2: Apply knowledge of mathematics and Engineering fundamentals to Identify and characterize different classes of signals

  • CO3: Identify, formulate the methodology to compute the response and analyze the properties of an LTI system

  • CO4: Identify Fourier Representations and analyze the signals in time and frequency domain for non periodic signals

  • CO5: Apply ZT for broader characterization of discrete time signals and LTI systems.

  • CO6: Demonstrate the basic concepts of signal processing using MATLAB/SCILAB



Unit I

Basics of Linear Algebra: Systems of Linear equations, Row reduction and Echelon forms, solutions to linear systems, Vectors in Rn, Linear combinations, the equation Ax=b, Linear independence Linear transformations (Text 1) 8 Hrs.

Unit II

Basics of Signals: Vector space, subspaces, Null spaces, column spaces, Bases, Spanning set. (Text1). Definition of signals and systems, mathematical representations, classification of signals, elementary signals. 8 Hrs.

Unit III

Discrete time systems : Operations on discrete time signals, Properties of discrete time systems, Impulse response representation of LTI Discrete time systems, Linear convolution of discrete time systems: Graphical method, properties of discrete time LTI systems in terms of impulse response representation, step response. 8 Hrs.

Unit IV

Fourier Transforms : Discrete time non periodic signals: DTFT and Inverse DTFT representations, continuous time non periodic signals: FT and IFT, properties of FT. 8 Hrs.

Unit V

Z-Transform: Introduction, Properties of ROC, Properties of Z-transform, inverse Z-transform (Partial fraction expansion method), Transform analysis of LTI systems, stability & causality. 7 Hrs

TEXT BOOK:


  1. David C. Lay Linear algebra and its applications, Ed 6, Pearson Education 2020

  2. Simon Haykin. Signals and systems. Ed 2. John Wiley.

REFERENCE BOOKS:

1 Schaum Series. Signals & Systems.

2 Oppenheim and Willsky. Signals & Systems.