Basic Signal Processing (21EC33)

Basic Signal Processing

Course Code: 21EC33
CIE Marks:50
Teaching Hours/Week (L: T: P: S):(3:0:2:0) 
SEE Marks:50
Total Hours of Pedagogy:40 hours Theory + 13 Lab slots 
Total Marks:100
Credits:04 
Exam Hours:03

Module-1

Vector Spaces: Vector spaces and Null subspaces, Rank and Row reduced form, Independence, Basis and dimension, Dimensions of the four subspaces, Rank-Nullity Theorem, Linear Transformations Orthogonality: Orthogonal Vectors and Subspaces, Projections and Least squares, Orthogonal Bases and Gram-Schmidt Orthogonalization procedure (Refer Chapters 2 and 3 of Text 1)

Module-2

Eigen values and Eigen vectors: Review of Eigen values and Diagonalization of a Matrix, Special Matrices (Positive Definite, Symmetric) and their properties, Singular Value Decomposition. (Refer Chapter 5, Text 1)

Module-3

Introduction and Classification of signals: Definition of signal and systems with examples, Elementary signals/Functions: Exponential, sinusoidal, step, impulse and ramp functions Basic Operations on signals: Amplitude scaling, addition, multiplication, time scaling, time shift and time reversal. Expression of triangular, rectangular and other waveforms in terms of elementary signals System Classification and properties: Linear-nonlinear, Time variant -invariant, causal-noncausal, static-dynamic, stable-unstable, invertible. (Text 2) [Only for Discrete Signals & Systems]

Module-4

Time domain representation of LTI System: Impulse response, convolution sum. Computation of convolution sum using graphical method for unit step and unit step, unit step and exponential, exponential and exponential, unit step and rectangular, and rectangular and rectangular. LTI system Properties in terms of impulse response: System interconnection, Memory less, Causal, Stable, Invertible and Deconvolution and step response (Text 2) [Only for Discrete Signals & Systems]

Module-5

The Z-Transforms: Z transform, properties of the region of convergence, properties of the Z-transform, Inverse Z-transform by partial fraction, Causality and stability, Transform analysis of LTI systems. (Text 2)

PRACTICAL COMPONENT OF IPCC

Sl.No Experiments

1 a. Program to create and modify a vector (array).

b. Program to create and modify a matrix.

2 Programs on basic operations on matrix.

3 Program to solve system of linear equations.

4 Program for Gram-Schmidt orthogonalization.

5 Program to find Eigen value and Eigen vector.

6 Program to find Singular value decomposition.

7 Program to generate discrete waveforms.

8 Program to perform basic operation on signals.

9 Program to perform convolution of two given sequences.

10 a. Program to perform verification of commutative property of convolution.

b. Program to perform verification of distributive property of convolution.

c. Program to perform verification of associative property of convolution.

11 Program to compute step response from the given impulse response.

12 Programs to find Z-transform and inverse Z-transform of a sequence.

Suggested Learning Resources:

Text Books

1. Gilbert Strang, “Linear Algebra and its Applications”, Cengage Learning, 4th Edition, 2006, ISBN 97809802327

2. Simon Haykin and Barry Van Veen, “Signals and Systems”, 2nd Edition, 2008, Wiley India. ISBN9971-51- 239-4.

Reference Books:

1. Michael Roberts, “Fundamentals of Signals & Systems”,2nd edition, Tata McGraw-Hill, 2010, ISBN978-0- 07-070221-9.

2. Alan V Oppenheim, Alan S WiIIsky and S Hamid Nawab, “Signals and Systems” Pearson Education Asia / PHI, 2"" edition, 1997. Indian Reprint 2002.

3. H P Hsu, R Ranjan, “Signals and Systems”, Schaum’s outlines, TMH, 2006.

4. B P Lathi, “Linear Systems and Signals”, Oxford University Press, 2005.

5. Ganesh Rao and Satish Tunga, “Signals and Systems”, Pearson/Sanguine.

6. Seymour Lipschutz, Marc Lipson, “Schaums Easy Outline of Linear Algebra”, 2020.

Web links and Video Lectures (e-Resources):

Video lectures on Signals and Systems by Alan V Oppenheim

Lecture 1, Introduction | MIT RES.6.007 Signals and Systems, Spring 2011 - YouTube

Lecture 2, Signals and Systems: Part 1 | MIT RES.6.007 Signals and Systems, Spring 2011 - YouTube

NPTEL video lectures signals and system:

https://www.youtube.com/watch?v=7Z3LE5uM-6Y&list=PLbMVogVj5nJQQZbah2uRZIRZ_9kfoqZyx

Video lectures on Linear Algebra by Gilbert Strang

https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715CB9EF31D&index=1