# Digital Signal Processing and its Applications

NPTEL and Indian Institute of Technology Bombay via YouTube

## 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