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Lecture 15C: PARTIAL FRACTION DECOMPOSITION
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Digital Signal Processing and Its Applications
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- 1 Course Introduction - Digital Signal Processing and its Applications
- 2 Lecture 1: Introduction: Digital signal processing and its objectives
- 3 Lecture 2A: Introduction to sampling and Fourier Transform
- 4 Lecture 2B: Sampling of sine wave and associate complication
- 5 Lecture 3A: Review of Sampling Theorem
- 6 Lecture 3B: Idealized Sampling, Reconstruction
- 7 Lecture 3C: Filters And Discrete System
- 8 Lecture 4A: Answering questions from previous lectures.
- 9 Lecture 4B: Desired requirements for discrete system
- 10 Lecture 4C: Introduction to phasors
- 11 Lecture 4D: Advantages of phasors in discrete systems
- 12 Lecture 5A: What do we want from a discrete system?
- 13 Lecture 5B: Linearity - Homogeneity and Additivity
- 14 Lecture 5C: Shift Invariance and Characterization of LTI systems
- 15 Lecture 6A: Characterization of LSI system using it’s impulse response
- 16 Lecture 6B: Introduction to convolution
- 17 Lecture 6C: Convolution:deeper ideas and understanding
- 18 Lecture 7A: Characterisation of LSI systems, Convolution-properties
- 19 Lecture 7B: RESPONSE OF LSI SYSTEMS TO COMPLEX SINUSOIDS
- 20 Lecture 7C: CONVERGENCE OF CONVOLUTION AND BIBO STABILITY
- 21 Lecture 8A: Commutativity & Associativity
- 22 Lecture 8B: BIBO Stability of an LSI system
- 23 Lecture 8C: Causality and memory of an LSI system.
- 24 Lecture 8D: Frequency response of an LSI system.
- 25 Lecture 9A: Introduction and conditions of Stability
- 26 Lecture 9B: Vectors and Inner Product.
- 27 Lecture 9C: Interpretation of Frequency Response as Dot Product
- 28 Lecture 9D: Interpretation ofFrequency Responseas Eigenvalues
- 29 Lecture 10A: Discrete time fourier transform
- 30 Lecture 10B: DTFT in LSI System and Convolution Theorem.
- 31 Lecture 10C: Definitions of sequences and Properties of DTFT.
- 32 Lecture 11A: Introduction to DTFT, IDTFT
- 33 Lecture 11B: Dual to convolution property
- 34 Lecture 11C: Multiplication Property, Introduction to Parseval’s theorem
- 35 Lecture 12A: Introduction And Property of DTFT
- 36 Lecture 12B: Review of Inverse DTFT
- 37 Lecture 12C: Parseval’s Theorem and energy and time spectral density
- 38 Lecture 13A: Discussion on Unit Step
- 39 Lecture 13B: Introduction to Z transform
- 40 Lecture 13C: Example of Z transform
- 41 Lecture 13D: Region of Convergence
- 42 Lecture 13E: Properties of Z transform
- 43 Lecture 14A: Z- Transform
- 44 Lecture 14B: Rational System
- 45 Lecture 15A: INTRODUCTION AND EXAMPLES OF RATIONAL Z TRANSFORM AND THEIR INVERSES
- 46 Lecture 15B: DOUBLE POLE EXAMPLES AND THEIR INVERSE Z TRANSFORM
- 47 Lecture 15C: PARTIAL FRACTION DECOMPOSITION
- 48 Lecture 15D: LSI SYSTEM EXAMPLES
- 49 Lecture 16A: Why are Rational Systems so important?
- 50 Lecture 16B: Solving Linear constant coefficient difference equations
- 51 Lecture 16C: Introduction to Resonance in Rational Systems
- 52 Lecture 17A: Characterization of Rational LSI system
- 53 Lecture 17B: Causality and stability of the ROC of the system function
- 54 Lecture 18A: RECAP OF RATIONAL SYSTEMS AND DISCRETE TIME FILTERS
- 55 Lecture 18B: SPECIFICATIONS FOR FILTER DESIGN
- 56 Lecture 18C: FOUR IDEAL PIECEWISE CONSTANT FILTERS
- 57 Lecture 18D: IMPORTANT CHARACTERISTICS OF IDEAL FILTERS
- 58 Lecture 19A: Synthesis of Discrete Time Filters, Realizable specifications
- 59 Lecture 19B: Realistic Specifications for low pass filter. Filter Design Process
- 60 Lecture 20A: Introduction to Filter Design. Analog IIR Filter, FIR and IIR discrete-time filter.
- 61 Lecture 20B: Analog to discrete transform
- 62 Lecture 20C: Intuitive transforms, Bilinear Transformation
- 63 Lecture 21A: Steps for IIR filter design
- 64 Lecture 21B: Analog filter design using Butterworth Approximation
- 65 Lecture 22A: Butterworth filter Derivation And Analysis of butterworth system function
- 66 Lecture 22B: Chebychev filter Derivation
- 67 Lecture 23: Midsem paper review discussion
- 68 Lecture 24A: The Chebyschev Approximation
- 69 Lecture 24B: Next step in design: Obtain poles
- 70 Lecture 25A: Introduction to Frequency Transformations in the Analog Domain
- 71 Lecture 25B: High pass transformation
- 72 Lecture 25C: Band pass transformation
- 73 Lecture 26A: Frequency Transformation
- 74 Lecture 26B: Different types of filters
- 75 Lecture 27A: Impulse invariant method and ideal impulse response
- 76 Lecture 27B: Design of FIR of length (2N+1) by the truncation method, Plotting the function V(w)
- 77 Lecture 28A: IIR filter using rectangular window, IIR filter using triangular window
- 78 Lecture 28B: Proof that frequency response of an fir filter using rectangular window function
- 79 Lecture 29A: Introduction to window functions
- 80 Lecture 29B: Examples of window functions
- 81 Lecture 29C: Explanation of Gibb’s Phenomenon and it’s application
- 82 Lecture 30A: Comparison of FIR And IIR Filter’s
- 83 Lecture 30B: Comparison of FIR And IIR Filter’s
- 84 Lecture 30C: Comparison of FIR And IIR Filter’s
- 85 Pseudo-Linear Phase Filter, Signal Flow Graph.
- 86 Lecture 31B: Comprehension of Signal Flow Graphs and Achievement of Pseudo Assembly Language Code.
- 87 Lecture 32A: Introduction to IIR Filter Realization and Cascade Structure
- 88 Lecture 32B: Cascade Parallel Structure
- 89 Lecture 32C: Lattice Structure
- 90 Lecture 33A: Recap And Review of Lattice Structure, Realization of FIR Function.
- 91 Lecture 33B: Backward recursion, Change in the recursive equation of lattice.
- 92 Lecture 34A: Lattice structure for an arbitrary rational system
- 93 Lecture 34B: Example realization of lattice structure for rational system
- 94 Lecture 35A: Introductory Remarks of Discrete Fourier Transform and Frequency Domain Sampling
- 95 Lecture 35B: Principle of Duality, The Circular Convolution
