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Fundamentals of Signal Processing by Minh N. Do - HTML preview
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Fundamentals of Signal Processing
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Fundamentals of Signal Processing
Table of Contents
Introduction to Fundamentals of Signal Processing
1
.
What is Digital Signal Processing?
Overview of Key Concepts in Digital Signal Processing
Chapter
1
.
Foundations
1.1
.
Signals Represent Information
Analog Signals
Digital Signals
1.2
.
Introduction to Systems
Cascade Interconnection
Parallel Interconnection
Feedback Interconnection
1.3
.
Discrete-Time Signals and Systems
Real- and Complex-valued Signals
Complex Exponentials
Sinusoids
Unit Sample
Unit Step
Symbolic Signals
Discrete-Time Systems
1.4
.
Linear Time-Invariant Systems
1.5
.
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
1.6
.
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
1.7
.
Hilbert Spaces
Hilbert Spaces
Examples of Hilbert Spaces
1.8
.
Signal Expansions
Main Idea
Alternate Representation
Finding the Coefficients
Simplifying our Equation
Examples
Extending the Dimension and Space
1.9
.
Introduction to Fourier Analysis
Fourier's Daring Leap
1.10
.
Continuous Time Fourier Transform (CTFT)
Introduction
Fourier Transform Synthesis
Equations
CTFT Definition Demonstration
Example Problems
Fourier Transform Summary
1.11
.
Discrete Time Fourier Transform (DTFT)
Introduction
DTFT synthesis
Equations
DTFT Definition demonstration
DTFT Summary
1.12
.
DFT as a Matrix Operation
Matrix Review
Representing DFT as Matrix Operation
1.13
.
The FFT Algorithm
The Fast Fourier Transform FFT
How does the FFT work?
Decimation in Time FFT
Derivation
Chapter
2
.
Sampling and Frequency Analysis
2.1
.
Introduction
Why sample?
Claude E. Shannon
Notation
The Sampling Theorem
2.2
.
Proof
Introduction
Proof part 1 - Spectral considerations
Proof part II - Signal reconstruction
Summary
2.3
.
Illustrations
Basic examples
The process of sampling
Sampling fast enough
Sampling too slowly
Reconstruction
Conclusions
2.4
.
Sampling and Reconstruction with Matlab
Matlab files
2.5
.
Systems View of Sampling and Reconstruction
Ideal reconstruction system
Ideal system including anti-aliasing
Reconstruction with hold operation
2.6
.
Sampling CT Signals: A Frequency Domain Perspective
Understanding Sampling in the Frequency Domain
Sampling
Relating x[n] to sampled x(t)
2.7
.
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
2.8
.
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
2.9
.
Short Time Fourier Transform
Short Time Fourier Transform
Sampled STFT
Spectrogram Example
Effect of window length R
Effect of L and N
Effect of R and L
2.10
.
Spectrograms
2.11
.
Filtering with the DFT
Introduction
Compute IDFT of Y[k]
DFT Pair
Regular Convolution from Periodic Convolution
DSP System
2.12
.
Image Restoration Basics
Image Restoration
Frequency Domain Analysis
Chapter
3
.
Digital Filtering
3.1
.
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