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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

Description:

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

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#Engineering #Electrical Engineering #Digital Signal Processing #Mathematics #Statistics & Probability #Sampling #Computer Science #Deep Learning #Convolution #Signal Processing #Z-Transform #Fourier Transform

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