Digital Signal Processing and its Applications

COURSE LAYOUT

Week 1: 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
Week 2: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
Week 3: 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 of Frequency Response as Eigenvalues
Week 4: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
Week 5: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

Week 6:Lecture 16A: Why are Rational Systems so important? Lecture 16B: Solving Linear constant coefficient difference equations which are valid over a finite range of time 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
Week 7: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 discrete-time filter, 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

Week 8: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

Week 9: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 centered at 0 is real.

Week 10: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 Lecture 31A: Introduction and approach to realization (causal rational system) Lecture 31B: Comprehension of Signal Flow Graphs and Achievement of Pseudo Assembly Language Code.

Week 11: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

Week 12:Lecture 35A: Introductory Remarks of Discrete Fourier Transform and Frequency Domain Sampling Lecture 35B: Principle of Duality, The Circular Convolution

TEACHING ASSISTANT
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