Digital Signal Processing

Signal Processing

What you'll learn

Discrete –Time Signals and Systems: Introduction to DSP, Advantages, basic elements of DSP system, sampling theorem, A/D, D/A conversion, quantization

Elementary discretetime sequences. Discrete-time systems: description, representation, classification (linear, time invariant, static, casual, stable)

Analysis of DTLTI systems: The convolution sum, properties of convolution, Analysis of causal LTI systems, stability of LTI systems, step response of LTI system

Difference equation, recursive & non recursive systems, solution of difference equations, Impulse response of LTI recursive system. Correlation of discrete time

z- Transform and Analysis of LTI Systems: Definition of z- Transform, properties, rational z-Transforms, evaluation of the inverse z- Transforms

Analysis of LTI systems in z-domain, transient and steady-state responses, causality, stability, pole-zero cancellation, the Schur-Cohn stability test

Fourier Transforms, the DFT and FFT: Definition & properties of Fourier transform, relation with z-transform. Finite duration sequences and DFT

Properties, circular convolution, Fast algorithms for the computation of DFT: radix-2 and radix- 4 FFT algorithms

Design of Digital Filters: Classification of filters: LP, HP, BP, FIR and IIR filters, filter specifications. Design Windows and by Frequency sampling methods

Design of IIR filters from Analog filters using approximation of derivatives, Impulse invariant transformation, Bilinear transformation and Matched z-Transform

Realization of Discrete-Time systems: Structures for realization of Discrete-Time systems, realization of FIR systems: Direct Form, Cascade Form,

Frequency sampling and Lattice structures. Realization of IIR filters: Direct Form, Signal flow graph and Transposed structures, Cascade form,

Lattice and Lattice ladder. Realization for IIR systems

Requirements

No prerequisite needed. You will learn everything you need to know.

Description

Discrete –Time Signals and Systems: Introduction to DSP, Advantages, basic elements of DSP system, sampling theorem, A/D, D/A conversion, quantization. Elementary discretetime sequences. Discrete-time systems: description, representation, classification (linear, timeinvariant, static, casual, stable)Analysis of DTLTI systems: The convolution sum, properties of convolution, Analysis of causal LTI systems, stability of LTI systems, step response of LTI systems, difference equation, recursive & non recursive discrete time systems, solution of difference equations, Impulse response of LTI recursive system. Correlation of discrete time signalsz- Transform and Analysis of LTI Systems: Definition of z- Transform, properties, rational z-Transforms, evaluation of the inverse z- Transforms, analysis of linear time invariant systems in z-domain, transient and steady-state responses, causality, stability, pole-zero cancellation, the Schur-Cohn stability testFourier Transforms, the DFT and FFT: Definition & properties of Fourier transform, relation with z-transform. Finite duration sequences and the discrete Fourier transform(DFT), properties, circular convolution, Fast algorithms for the computation of DFT: radix-2 and radix4 FFT algorithmsDesign of Digital Filters: Classification of filters: LP, HP, BP, FIR and IIR filters, filter specifications. Design of FIR filters using Windows and by Frequency sampling methods. Design of IIR filters from Analog filters using approximation of derivatives, Impulse invariant transformation, Bilinear transformation and Matched z-Transformation, Commonly used Analog filters and IIR Filter design exampleRealization of Discrete-Time systems: Structures for realization of Discrete-Time systems, realization of FIR systems: Direct Form, Cascade Form, Frequency sampling and Lattice structures. Realization of IIR filters: Direct Form, Signal flow graph and Transposed structures, Cascade form, Lattice and Lattice ladder. Realization for IIR systems

Overview

Section 1: Discrete –Time Signals and Systems

Lecture 1 Introduction to Digital Signal Processing, Digital Signal, Analog Signal

Lecture 2 Signal Examples. Definition: Signal, Signal Source, System, Signal Processing

Lecture 3 Basic Elements of Digital Signal Processing System

Lecture 4 Analog to Digital Conversion, Digital to Analog Conversion, Sampling

Lecture 5 Sampling of Analog Signal, Sampling Theorem, Sampling Frequency, Aliasing Effect

Lecture 6 Example on Sampling Theorem, Identifying Sampling Frequency, Nyquist Rate

Lecture 7 Quantization of Continuous Amplitude Signal, Coding, Quantization Error

Lecture 8 Discrete Time Signals, Representations of Discrete Time Signal

Lecture 9 Elementary Discrete Time Signals

Lecture 10 Discrete Time Systems, Identifying Response of Discrete Time System

Lecture 11 Block Diagram Representation of Discrete-time Systems, Basic Building Blocks

Lecture 12 Block Diagram Representation of Discrete-time System, Realization

Lecture 13 Classification of Discrete-Time Systems

Lecture 14 Time invariant versus time variant systems

Lecture 15 Linear Versus Non-linear Systems

Lecture 16 Causal Systems, Non-causal Systems

Lecture 17 Stable Versus Unstable Systems

Lecture 18 Classification of Signals

Section 2: Analysis of Discrete-Time Linear Time-Invariant Systems

Lecture 19 Analysis of Discrete-Time Linear Time-Invariant Systems

Lecture 20 Response of Discrete-Time Linear Time-Invariant Systems

Lecture 21 Convolution Sum, Identification of Convolution

Lecture 22 Convolution Sum, Identification of Convolution

Lecture 23 Convolution Sum, Identification of Convolution

Lecture 24 Properties of Convolution

Lecture 25 Causal Linear Time-Invariant Systems

Lecture 26 Stability of Linear Time Invariant Systems

Lecture 27 Systems with Finite Duration and Infinite Duration Impulse Response

Lecture 28 Discrete-Time Systems Described by Difference Equations

Lecture 29 Recursive and Non-recursive Discrete Time Systems

Lecture 30 LTI Systems Characterized by Constant-Coefficient Difference Equations

Lecture 31 Solution of Linear Constant-Coefficient Difference Equations

Lecture 32 Identifying homogeneous solution from first order difference equation

Lecture 33 Identifying homogeneous solution from second order difference equation

Lecture 34 The Particular Solution of Difference Equation

Lecture 35 The Particular Solution of Difference Equation

Lecture 36 The Total Solution of The Difference Equation

Lecture 37 Total Response of the Linear Time Invariant System

Lecture 38 Impulse Response of Linear Time-Invariant Recursive Systems

Lecture 39 The Impulse Response of a Linear Time-Invariant Recursive System

Lecture 40 Correlation of Discrete-Time Signals, Cross Correlation, Auto Correlation

Lecture 41 Correlation of Discrete-Time Signals, Cross Correlation Example

Lecture 42 Auto-correlation of Discrete-Time Signal, Correlation of Discrete-Time Signals

Undergraduate and Post Graduate Students