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# Digital Signal Processing and its Applications

### Overview

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.
INTENDED AUDIENCE :
Third Year Undergraduates/ First Year Graduate (Masters’ Students)PREREQUISITES : It would help if they have an exposure to ‘Signals and Systems’, although this is not a strict pre-requisite.
INDUSTRIES SUPPORT :Texas Instruments, Analog Devices, Samsung, almost any industry which works in communication and signal processing would value this training, as a core discipline.

### 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

### Taught by 