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NPTEL

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

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