Digital Signal Processing and its Applications

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