Tài liệu

# Fundamentals of Signal Processing

Mathematics and Statistics

# Outline

1. Foundations
1. Signals Represent Information
2. Introduction to Systems
3. Discrete-Time Signals and Systems
4. Linear Time-Invariant Systems
5. Discrete-Time Convolution
6. Review of Linear Algebra
7. Hilbert Spaces
8. Signal Expansions
9. Fourier Analysis
10. Continuous-Time Fourier Transform (CTFT)
11. Discrete-Time Fourier Transform (DTFT)
12. DFT as a Matrix Operation
13. The FFT Algorithm
14. Solutions
2. Sampling and Frequency Analysis
1. Introduction
2. Proof
3. Illustrations
4. Sampling and Reconstruction with Matlab
5. Systems View of Sampling and Reconstruction
6. Sampling CT Signals: A Frequency Domain Perspective
7. The DFT: Frequency Domain with a Computer Analysis
8. Discrete-Time Processing of CT Signals
9. Short Time Fourier Transform
10. Spectrograms
11. Filtering with the DFT
12. Image Restoration Basics
13. Solutions
3. Digital Filtering
1. Difference Equation 103
2. The Z Transform: Definition
3. Table of Common z-Transforms
4. Understanding Pole/Zero Plots on the Z-Plane
5. Filtering in the Frequency Domain
6. Linear-Phase FIR Filters
7. Filter Structures
8. Overview of Digital Filter Design
9. Window Design Method 125
10. Frequency Sampling Design Method for FIR Filters
11. Parks-McClellan FIR Filter Design
12. FIR Filter Design using MATLAB
13. MATLAB FIR Filter Design Exercise
14. Solutions
4. Statistical and Adaptive Signal Processing
1. Introduction to Random Signals and Processes
2. Stationary and Nonstationary Random Processes
3. Random Processes: Mean and Variance
4. Correlation and Covariance of a Random Signal
5. Autocorrelation of Random Processes
6. Crosscorrelation of Random Processes
8. Discrete-Time, Causal Wiener Filter
9. Practical Issues in Wiener Filter Implementation
11. The LMS Adaptive Filter Algorithm
12. First Order Convergence Analysis of the LMS Algorithm

Solutions

Glossary

Bibliography

Index

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