# Digital Signal Processing and its Applications

By Prof. V. M. Gadre   |   IIT Bombay
Learners enrolled: 3102
The course begins with a discussion on Discrete Time signals and systems. This is followed by an introduction of the Z transform, its properties and system theoretic implications. The foundations of digital filter design and realization are built up. Practice Problems with solutions, summaries of each lecture and illustrative explanations of concepts are all additionally provided, to enhance learning.

INTENDED AUDIENCE
PREREQUISITES : It would help if they have an exposure to ‘Signals and Systems’, although this is not a strict pre-requisite.
INDUSTRIES  SUPPORT     : Texas Instruments, Analog Devices, Samsung, almost any industry which works in communication and signal processing would value this training, as a core discipline.
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Start Date : 18 Jan 2021 End Date : 09 Apr 2021 Exam Date : 24 Apr 2021 IST Enrollment Ends : 01 Feb 2021 Category : Electrical, Electronics and Communications Engineering Communication and Signal Processing Credit Points : 3 Level : Undergraduate/Postgraduate

### Course layout

Week 1:  Lecture 1: Introduction: Digital signal processing and its objectives
Lecture 2A: Introduction to sampling and Fourier Transform
Lecture 2B: Sampling of sine wave and associate complication
Lecture 3A: Review of  Sampling Theorem
Lecture 3B: Idealized Sampling, Reconstruction
Lecture 3C: Filters And  Discrete System
Week 2:  Lecture 4A: Answering questions from previous lectures.
Lecture 4B: Desired requirements for discrete system
Lecture 4C: Introduction to phasors
Lecture 4D:  Advantages of phasors in discrete systems
Lecture 5A: What do we want from a discrete system?
Lecture 5B:  Linearity - Homogeneity and Additivity
Lecture 5C: Shift Invariance and Characterization of LTI systems
Lecture 6A: Characterization of LSI system using it’s impulse response
Lecture 6B: Introduction to convolution
Lecture 6C: Convolution: deeper ideas and understanding

Week 3:  Lecture 7A: Characterisation of LSI systems, Convolution-properties
Lecture 7B: Response of LSI systems to complex sinusoids
Lecture 7C: Convergence of convolution and BIBO stability
Lecture 8A: Commutativity & Associativity
Lecture 8B: BIBO Stability of an LSI system
Lecture 8C: Causality and memory of an LSI system.
Lecture 8D: Frequency response of an LSI system.
Lecture 9A: Introduction and conditions of Stability
Lecture 9B: Vectors and Inner Product.
Lecture 9C: Interpretation of frequency Response as Dot Product
Lecture 9D: Interpretation of Frequency Response as Eigenvalues

Week 4:  Lecture 10A: Discrete time fourier transform
Lecture 10B: DTFT in LSI System and Convolution Theorem.
Lecture 10C: Definitions of sequences and Properties of DTFT.
Lecture 11A: Introduction to DTFT,  IDTFT
Lecture 11B: Dual to convolution property
Lecture 11C: Multiplication Property, Introduction to Parseval’s theorem
Lecture 12A: Introduction And Property of DTFT
Lecture 12B: Review of Inverse DTFT
Lecture 12C: Parseval’s Theorem and energy and time spectral density

Week 5:  Lecture 13A: Discussion on Unit Step
Lecture 13B: Introduction to Z transform
Lecture 13C: Example of Z transform
Lecture 13D: Region of Convergence
Lecture 13E: Properties of Z transform
Lecture 14A: Z- Transform
Lecture 14B: Rational System
Lecture 15A: Introduction And Examples Of Rational Z Transform And Their Inverses
Lecture 15B: Double Pole Examples And Their Inverse Z Transform
Lecture 15C: Partial Fraction Decomposition
Lecture 15D: LSI System Examples

Week 6:  Lecture 16A: Why are Rational Systems so important?
Lecture 16B: Solving Linear constant coefficient difference equations which are valid over a finite range of time
Lecture 16C: Introduction to Resonance in Rational Systems
Lecture 17A: Characterization of Rational LSI system
Lecture 17B: Causality and stability of the ROC of the system function
Lecture 18A: Recap Of Rational Systems And Discrete Time  Filters
Lecture 18B: Specifications For Filter Design
Lecture 18C: Four Ideal Piecewise Constant Filters
Lecture 18D: Important Characteristics Of Ideal Filters

Week 7:  Lecture 19A: Synthesis of Discrete Time Filters, Realizable specifications
Lecture 19B: Realistic Specifications for low pass filter. Filter Design Process
Lecture 20A: Introduction to Filter Design. Analog IIR Filter,FIR discrete-time filter, IIR discrete-time filter.
Lecture 20B: Analog to discrete transform
Lecture 20C: Intuitive transforms, Bilinear Transformation
Lecture 21A: Steps for IIR filter design
Lecture 21B: Analog filter design using Butterworth Approximation

Week 8:  Lecture 22A: Butterworth filter Derivation And Analysis of butterworth system function
Lecture 22B: Chebychev filter Derivation
Lecture 23: Midsem paper review discussion
Lecture 24A: The Chebyschev Approximation
Lecture 24B: Next step in design: Obtain poles
Lecture 25A: Introduction to Frequency Transformations in the Analog Domain
Lecture 25B: High pass transformation
Lecture 25C: Band pass transformation

Week 9:  Lecture 26A: Frequency Transformation
Lecture 26B: Different types of  filters
Lecture 27A: Impulse invariant method and ideal impulse response
Lecture 27B: Design of FIR of length (2N+1) by the truncation method,Plotting the function V(w)
Lecture 28A: IIR filter using rectangular window, IIR filter using triangular window
Lecture 28B: Proof that frequency response of an fir filter using rectangular window function centered at 0 is real.

Week 10:  Lecture 29A: Introduction to window functions
Lecture 29B: Examples of window functions
Lecture 29C: Explanation of Gibb’s Phenomenon and it’s application
Lecture 30A: Comparison of FIR And IIR Filter’s
Lecture 30B: Comparison of FIR And IIR Filter’s
Lecture 30C: Comparison of FIR And IIR Filter’s
Lecture 31A: Introduction and approach to realization (causal rational system)
Lecture 31B: Comprehension of Signal Flow Graphs and Achievement of Pseudo Assembly Language Code.

Week 11:  Lecture 32A: Introduction to IIR Filter Realization and Cascade Structure
Lecture 32C: Lattice Structure
Lecture 33A: Recap And Review of Lattice Structure, Realization of FIR Function.
Lecture 33B: Backward recursion, Change in the recursive equation of lattice.
Lecture 34A: Lattice structure for an arbitrary rational system
Lecture 34B: Example realization of lattice structure for rational system

Week 12:  Lecture 35A: Introductory Remarks of Discrete Fourier Transform and Frequency Domain Sampling
Lecture 35B: Principle of Duality, The Circular Convolution

TEACHING ASSISTANT

### Books and references

1. Alan V. Oppenheim, Ronald W. Schafer – “Discrete Time Signal Processing”, Prentice Hall of India (Private) Limited, New Delhi, 1994 (c1989). This book was earlier entitled “Digital Signal Processing” and one may consult/ use this earlier version if the current title is unavailable.
2. John G. Proakis, Dimitris G. Manolakis – “Digital Signal Processing – Principles, Algorithms and Applications”, Third Edition, Prentice Hall of India Private Limited, New Delhi – 110 001, 1997, Eastern Economy Edition. An excellent text with a very detailed explanation of ideas. Develops the subject very thoroughly with a comprehensive set of solved examples. A subsequent (fourth) edition of the book is also available in Eastern Economy Edition now.
3. Sanjit K. Mitra, “Digital Signal Processing – A computer based approach”, Mc Graw Hill International Edition, Second Edition, 2001, Electrical Engineering Series. This book is likely to be available as a Tata Mc Graw-Hill Edition too. An excellent textbook and reference book. It deals with an extensive set of applications, problems and builds concepts very firmly.
4. Sanjit K. Mitra, “Digital Signal Processing Laboratory using MATLAB”, Mc Graw Hill International Edition, 2000, Computer Science Series. A good laboratory supplement to a theory course.
5. James H. McClellan, Ronald W. Schafer, Mark A. Yoder, “DSP First: A Multimedia Approach”, Prentice Hall, NJ, (c 1998 by Prentice Hall). Blends theory and application examples nicely.
6. Vinay K. Ingle, John G. Proakis, “Digital Signal Processing Using MATLAB”, (c 2000 by Brooks/Cole), Brooks/Cole Publishing Company, a division of Thomson Learning. A good laboratory supplement to a theory course.
7. Monson H. Hayes, Schaum’s Outlines of Theory and Problems of Digital Signal Processing, Mc Graw Hill Publishing Company, (c 1999). Provides a number of solved examples.
8. David J. De Fatta, Joseph G. Lucas, William S. Hodgkiss, “Digital Signal Processing- A System Design Approach”, John Wiley and Sons, Inc. Pte. Ltd., Singapore. A good book from an applications perspective, with system design with DSP emphasized.
9. Johnny R. Johnson, “Introduction to Digital Signal Processing”, Prentice Hall of India Private Limited, New Delhi – 110 001, 1994, Eastern Economy Edition. A lucid, introductory text with an excellent treatment for beginners. Also has good solved examples.
10. Lawrence R. Rabiner, Bernard Gold, “Theory and application of Digital Signal Processing”, Prentice Hall of India Private Limited, New Delhi – 110 001, 1993, Eastern Economy Edition. This book would serve as a detailed reference for filter design. It may not be suitable as a text, for want of exercises to solve.
11. Thomas J. Cavicchi, “Digital Signal Processing”, John Wiley and Sons (Pte.) Limited: available in inexpensive Indian Edition. A fairly detailed and insightful text.
12. Jonathan (Y) Stein, “Digital Signal Processing – A Computer Science Perspective”, Wiley Student Edition, John Wiley and Sons (Asia) Pte Ltd. Available in inexpensive Indian Edition. It gives some reasonably detailed descriptions of applications, and architectures for Digital Signal Processing.
13. Avtar Singh, S. Srinivasan, “Digital Signal Processing – Implementations Using DSP Microprocessors with Examples from TMS320C54xx, Thomson Brooks/ Cole, Copyright 2004, ISBN: 981-243-254-4. This reprint is for sale in the Indian Subcontinent only. It is a very useful text to proceed from theory to design and implementation of systems on digital signal processors.

### Instructor bio

IIT Bombay
Prof. Vikram M. Gadre is currently a Professor at Department of Electrical Engineering, IIT Bombay. He received his Undergraduate degree, along with President’s Gold Medal for cumulative performance during his B.Tech, from IIT Delhi in 1989. He received his PhD degree in Electrical Engineering from Indian Institute of Technology, Delhi in 1994.
His research interests are Communication and signal processing, with emphasis on multiresolution and multi-rate signal processing, especially wavelets and filter banks: theory and applications. He is known for his unique way of teaching for which he received Award for Excellence in Teaching four times from IIT Bombay.
His other recognitions and awards include: S.S.I. Varshney Award from the Systems Society of India (S.S.I) (2011), IIT Bombay Research Paper Award (2008), Felicitation from Society for Cancer Research and Communication (SCRAC), India (2006), Sixth SVC Aiya Memorial Award for Telecom Education from IETE Pune Centre (2005), 11th IETE Prof K Sreenivasan Memorial Award(2004), INAE Young Engineer Award from the Indian National Academy of Engineers (2001), Student Journal Award of the IETE(1994), Adarsh Ratna Bhagat Award from National Service Scheme,IIT Delhi(1992)

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 April 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team