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Digital Signal Processing: A User's Guide by Douglas L. Jones. - HTML preview
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Digital Signal Processing: A User's Guide
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Digital Signal Processing: A User's Guide
Table of Contents
Preface for Digital Signal Processing: A User's Guide
1
.
Chapter
1
.
Background, Review, and Reference
1.1
.
Discrete-Time Signals and Systems
Real- and Complex-valued Signals
Complex Exponentials
Sinusoids
Unit Sample
Unit Step
Symbolic Signals
Discrete-Time Systems
1.2
.
Systems in the Time-Domain
1.3
.
Discrete Time Convolution
Introduction
Convolution and Circular Convolution
Convolution
Operation Definition
Definition Motivation
Graphical Intuition
Circular Convolution
Definition Motivation
Graphical Intuition
Interactive Element
Convolution Summary
1.4
.
Review of Linear Algebra
Fields
Examples
Vector Spaces
Examples
Euclidean Space
Real Euclidean space
Complex Euclidean space
Subspaces
Linear Independence
Spanning Sets
Aside
Bases
Key Fact
Other Facts
Dimension
Examples
Direct Sums
Facts
Proofs
Norms
Examples
Induced Metric
Inner products
Examples
Triangle Inequality
Cauchy-Schwarz Inequality
Orthogonality
Orthonormal Bases
Expansion Coefficients
Gram-Schmidt
Orthogonal Compliments
Linear Transformations
Image
Nullspace
Rank
Nullity
Rank plus nullity theorem
Matrices
Column span
Duality
Inverses
1.5
.
Orthonormal Basis Expansions
Main Idea
Alternate Representation
Finding the Coefficients
Simplifying our Equation
Examples
Extending the Dimension and Space
1.6
.
Introduction to Fourier Analysis
Fourier's Daring Leap
1.7
.
Continuous Time Fourier Transform (CTFT)
Introduction
Fourier Transform Synthesis
Equations
CTFT Definition Demonstration
Example Problems
Fourier Transform Summary
1.8
.
Discrete-Time Fourier Transform (DTFT)
1.9
.
DFT as a Matrix Operation
Matrix Review
Representing DFT as Matrix Operation
1.10
.
Sampling theory
Introduction
Why sample?
Claude E. Shannon
Notation
The Sampling Theorem
Proof
Introduction
Proof part 1 - Spectral considerations
Proof part II - Signal reconstruction
Summary
Illustrations
Basic examples
The process of sampling
Sampling fast enough
Sampling too slowly
Reconstruction
Conclusions
Systems view of sampling and reconstruction
Ideal reconstruction system
Ideal system including anti-aliasing
Reconstruction with hold operation
Sampling CT Signals: A Frequency Domain Perspective
Understanding Sampling in the Frequency Domain
Sampling
Relating x[n] to sampled x(t)
The DFT: Frequency Domain with a Computer Analysis
Introduction
Sampling DTFT
Choosing M
Case 1
Case 2
Discrete Fourier Transform (DFT)
Interpretation
Remark 1
Remark 2
Periodicity of the DFT
A Sampling Perspective
Inverse DTFT of S(ω)
Connections
Discrete-Time Processing of CT Signals
DT Processing of CT Signals
Analysis
Summary
Note
Application: 60Hz Noise Removal
DSP Solution
Sampling Period/Rate
Digital Filter
1.11
.
Z-Transform
Difference Equation
Introduction
General Formulas for the Difference Equation
Difference Equation
Conversion to Z-Transform
Conversion to Frequency Response
Example
Solving a LCCDE
Direct Method
Homogeneous Solution
Particular Solution
Indirect Method
The Z Transform: Definition
Basic Definition of the Z-Transform
The Complex Plane
Region of Convergence
Table of Common z-Transforms
Understanding Pole/Zero Plots on the Z-Plane
Introduction to Poles and Zeros of the Z-Transform
The Z-Plane
Examples of Pole/Zero Plots
Interactive Demonstration of Poles and Zeros
Applications for pole-zero plots
Stability and Control theory
Pole/Zero Plots and the Region of Convergence
Frequency Response and Pole/Zero Plots
1.12
.
Random Signals and Processes
Introduction to Random Signals and Processes
Signals: Deterministic vs. Stochastic
Deterministic Signals
Stochastic Signals
Random Process
Stationary and Nonstationary Random Processes
Introduction
Distribution and Density Functions
Stationarity
First-Order Stationary Process
Second-Order and Strict-Sense Stationary Process
Wide-Sense Stationary Process
Random Processes: Mean and Variance
Mean Value
Properties of the Mean
Mean-Square Value
Variance
Standard Deviation
Properties of Variance
Time Averages
Estimating the Mean
Estimating the Variance
Example
Correlation and Covariance of a Random Signal
Covariance
Useful Properties
Correlation
Corre
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