ECE 454 and ECE 554 Supplemental reading
Collection edited by: Thad Welch
Content authors: Don Johnson, Minh Do, C. Burrus, Roy Ha, Michael Haag, Nguyen Huu
Phuong, Richard Baraniuk, Melissa Selik, Nasser Kehtarnavaz, Philipos Loizou, Mohammad
Rahman, Anders Gjendemsjø, Robert Nowak, Justin Romberg, Stephen Kruzick, Mark Davenport,
Tuan Do-Hong, Ricardo Radaelli-Sanchez, Catherine Elder, Ivan Selesnick, Benjamin Fite,
Douglas Jones, Swaroop Appadwedula, Matthew Berry, Mark Haun, Jake Janevitz, Michael
Kramer, Dima Moussa, Daniel Sachs, and Brian Wade
Online: < http://cnx.org/content/col11416/1.1>
This selection and arrangement of content as a collection is copyrighted by Thad Welch.
It is licensed under the Creative Commons Attribution License: http://creativecommons.org/licenses/by/3.0/
Collection structure revised: 2012/04/02
For copyright and attribution information for the modules contained in this collection, see the " Attributions" section at the end of the collection.
ECE 454 and ECE 554 Supplemental reading
Table of Contents
Chapter 1. ECE 454/ECE 554 Supplemental Reading for Chapter 1
1.1. Introduction to Digital Signal Processing
1.2. Introduction to Fundamentals of Signal Processing
What is Digital Signal Processing?
Overview of Key Concepts in Digital Signal Processing
1.3. m09 - An Overview of Discrete-Time Signals
[Discrete-Time Signals]Discrete-Time Signals
Chapter 2. ECE 454/ECE 554 Supplemental Reading for Chapter 2
XSL Transformations and Macros
2.2. Discrete-Time Systems in the Time-Domain
2.3. Signals Represent Information
2.5. Discrete-Time Signals and Systems
Real- and Complex-valued Signals
2.6. Systems in the Time-Domain
2.7. Autocorrelation of Random Processes
Estimating the Autocorrleation with Time-Averaging
Cross-correlation and auto-correlation
Correlation and data communication
Correlation of periodic signals
Chapter 3. ECE 454/ECE 554 Supplemental Reading for Chapter 3
3.2. Discrete-Time Fourier Transform (DTFT)
3.3. Continuous Time Fourier Transform (CTFT)
3.4. Discrete Time Fourier Transform (DTFT)
3.5. Continuous-Time Fourier Transform
Numerical Approximations to CTFT
Proof part 1 - Spectral considerations
Proof part II - Signal reconstruction
3.9. Sampling and reconstruction with Matlab
3.10. Systems view of sampling and reconstruction
Ideal system including anti-aliasing
Reconstruction with hold operation
3.11. Sampling CT Signals: A Frequency Domain Perspective
Understanding Sampling in the Frequency Domain
Sampling of continuous-time signals
3.13. The DFT: Frequency Domain with a Computer Analysis
Discrete Fourier Transform (DFT)
Nyquist-Shannon Sampling Theorem
Statement of the Sampling Theorem
Discrete Time Processing of Continuous Time Signals
Chapter 4. ECE 454/ECE 554 Supplemental Reading for Chapter 4
4.1. Examples for Systems in the Time Domain
4.2. Discrete-Time Processing of CT Signals
Application: 60Hz Noise Removal
Derivation of the Convolution Sum
The Matrix Formulation of Convolution
The Z-Transform Transfer Function
Frequency Response of Discrete-Time Systems
Fundamental Theorem of Linear, Time-Invariant Systems
Relation of PZ Plots, FR Plots, Impulse R
4.4. Eigenvectors of LSI Systems
Understanding Conditions on Matrix for Shift Invariance
Summary: LSI Systems and Imuplse Response
4.6. System Classifications and Properties
Time Invariant vs. Time Variant
Difference Equation Representation
4.8. PROPERTIES OF THE DIGITAL CONVOLUTION
Impulse response for causal system and signal
4.9. Discrete Time Convolution
Convolution and Circular Convolution
4.10. Linear-Phase FIR Filters
4.11. m21 - Convolution of Discrete-Time Signals
Derivation of the Convolution Sum
The Matrix Formulation of Convolution
Chapter 5. ECE 454/ECE 554 Supplemental Reading for Chapter 5
5.1. DFT as a Matrix Operation
Representing DFT as Matrix Operation
Regular Convolution from Periodic Convolution
5.3. m10 - The Discrete Fourier Transform
The Discrete Fourier Transform
Complex Sinusoids in a nutshell
5.5. INTRODUCTORY DISCRETE FOURIER TRANSFORM (DFT)
INTRODUCTORY DISCRETE FOURIER TRANSFORM (DFT)
The Discrete Fourier Transform
The Discrete-Time Fourier Transform
Evaluation of the DTFT by the DFT
Solution of Difference Equations using the Z-Transform
Region of Convergence for the Z-Transform
Relation of the Z-Transform to the DTFT and the DFT
Relationships Among Fourier Transforms
Generalization of the Basic Wavelet System
5.7. Efficiency of Frequency-Domain Filtering
5.8. Conclusions: Fast Fourier Transforms
5.9. The Cooley-Tukey Fast Fourier Transform Algorithm
Modifications to the Basic Cooley-Tukey FFT
Evaluation of the Cooley-Tukey FFT Algorithms
The Quick Fourier Transform, An FFT based on Symmetries
Further Reductions if the Length is Even
Arithmetic Complexity and Timings
5.11. Short Time Fourier Transform
5.13. m19 - Wavlet-Based Signal Analysis
Generalization of the Basic Wavelet System
Chapter 6. ECE 454/ECE 554 Supplemental Reading for Chapter 6
Real- and Complex-valued Signals
General Formulas for the Difference Equation
Conversion to Frequency Response
6.3. The Z Transform: Definition
Basic Definition of the Z-Transform
6.4. Table of Common z-Transforms
6.5. Understanding Pole/Zero Plots on the Z-Plane
Introduction to Poles and Zeros of the Z-Transform
Interactive Demonstration of Poles and Zeros
Applications for pole-zero plots
Pole/Zero Plots and the Region of Convergence
Frequency Response and Pole/Zero Plots
Relation of the Z-Transform to the DTFT and the DFT
General Formulas for the Differential Equation
Conversion to Laplace-Transform
Conversion to Frequency Response
Chapter 7. ECE 454/ECE 554 Supplemental Reading for Chapter 7
7.1. Filtering in the Frequency Domain
7.2. FREQUENCY RESPONSE OF LTI (LSI) SYSTEMS
Magnitude frequency response on decibel scale
Eigen-function and eigen-value in DSP systems
Frequency response of systems in cascade or in parallel
Frequency response in terms of filter coefficients
7.3. FREQUENCY RESPONSE OF LTI (LSI) SYSTEMS