COURSE OUTLINE: 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.

# Digital Signal Processing and its Applications

NPTEL and Indian Institute of Technology Bombay via YouTube

### Overview

### Syllabus

Course Introduction - Digital Signal Processing and its Applications.

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.

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.

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 ofFrequency Responseas Eigenvalues.

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.

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.

Lecture 16A: Why are Rational Systems so important?.

Lecture 16B: Solving Linear constant coefficient difference equations.

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.

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 and 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.

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.

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.

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.

Pseudo-Linear Phase Filter, Signal Flow Graph..

Lecture 31B: Comprehension of Signal Flow Graphs and Achievement of Pseudo Assembly Language Code..

Lecture 32A: Introduction to IIR Filter Realization and Cascade Structure.

Lecture 32B: Cascade Parallel 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.

Lecture 35A: Introductory Remarks of Discrete Fourier Transform and Frequency Domain Sampling.

Lecture 35B: Principle of Duality, The Circular Convolution.

### Taught by

IIT Bombay July 2018