Fundamentals of Signal Processing

Mathematics and Statistics


  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
    7. Introduction to Adaptive Filters
    8. Discrete-Time, Causal Wiener Filter
    9. Practical Issues in Wiener Filter Implementation
    10. Quadratic Minimization and Gradient Descent
    11. The LMS Adaptive Filter Algorithm
    12. First Order Convergence Analysis of the LMS Algorithm
    13. Adaptive Equalization





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