21EC33 Basic Signal Processing syllabus for EC

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

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.

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.

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

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.

PRACTICAL COMPONENT OF IPCC

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.

Course outcomes (Course Skill Set)

At the end of the course the student will be able to :

1. Understand the basics of Linear Algebra

2. Analyse different types of signals and systems

3. Analyse the properties of discrete-time signals & systems

4. Analyse discrete time signals & systems using Z transforms

Assessment Details (both CIE and SEE)

• The weightage of Continuous Internal Evaluation (CIE) is 50% and for Semester End Exam (SEE) is 50%.
• The minimum passing mark for the CIE is 40% of the maximum marks (20 marks).
• A student shall be deemed to have satisfied the academic requirements and earned the credits allotted to each subject/ course if the student secures not less than 35% (18 Marks out of 50) in the semester-end examination (SEE), and a minimum of 40% (40 marks out of 100) in the sum total of the CIE (Continuous Internal Evaluation) and SEE (Semester End Examination) taken together

CIE for the theory component of IPCC

Two Tests each of 20 Marks (duration 01 hour)

• First test at the end of 5th week of the semester
• Second test at the end of the 10th week of the semester

Two assignments each of 10 Marks

• First assignment at the end of 4th week of the semester
• Programming assignment at the end of 9th week of the semester, which can be implemented using programming languages like C++/Python/Java/Scilab Scaled-down marks of two tests and two assignments added will be CIE marks for the theory component of IPCC for 30 marks.

CIE for the practical component of IPCC

• On completion of every experiment/program in the laboratory, the students shall be evaluated and marks shall be awarded on the same day. The 15 marks are for conducting the experiment and preparation of the laboratory record, the other 05 marks shall be for the test conducted at the end of the semester.
• The CIE marks awarded in the case of the Practical component shall be based on the continuous evaluation of the laboratory report. Each experiment report can be evaluated for 10 marks. Marks of all experiments’ write-ups are added and scaled down to 15 marks.
• The laboratory test (duration 03 hours) at the end of the 15th week of the semester /after completion of all the experiments (whichever is early) shall be conducted for 50 marks and scaled down to 05 marks. Scaled-down marks of write-up evaluations and tests added will be CIE marks for the laboratory component of IPCC for 20 marks.

SEE for IPCC

Theory SEE will be conducted by University as per the scheduled timetable, with common question papers for the course (duration 03 hours)

• The question paper will have ten questions. Each question is set for 20 marks.
• There will be 2 questions from each module. Each of the two questions under a module (with a maximum of 3 sub-questions), should have a mix of topics under that module.
• The students have to answer 5 full questions, selecting one full question from each module.

The theory portion of the IPCC shall be for both CIE and SEE, whereas the practical portion will have a CIE component only. Questions mentioned in the SEE paper shall include questions from the practical component.

• The minimum marks to be secured in CIE to appear for SEE shall be the 12 (40% of maximum marks-30) in the theory component and 08 (40% of maximum marks -20) in the practical component. The laboratory component of the IPCC shall be for CIE only. However, in SEE, the questions from the laboratory component shall be included. The maximum of 04/05 questions to be set from the practical component of IPCC, the total marks of all questions should not be more than the 20 marks.

SEE will be conducted for 100 marks and students shall secure 35% of the maximum marks to qualify in the SEE. Marks secured out of 100 will be scaled down to 50 marks.

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.