Notation, Symbols, and Abbreviations 

How to Learn Signal Processing with allsignalprocessing.com

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** denotes lessons available with introductory membership

Part 1

Essentials and Professional levels

Foundations

1. Signals Everywhere**
2. Ever-Present Noise**
3. Models, Math, and Real-World Signals**
4. Four Signal-Processing Themes**
5. Building Signals with Blocks: Basis Expansions**
6. Signals: The Basics**
7. Sinusoidal Signals**
8. Sinusoidal Signals Examples**
9. Complex Sinusoids**
10. Exponential, Step, and Impulse Signals**
11. Introduction to Linear, Time-Invariant Systems**
12. Introduction to Difference Equation System Descriptions**
13. Impulse Response Descriptions for LTI Systems**
14. Frequency Response Descriptions for LTI Systems**
15. Introduction to the System Function and System Poles and Zeros**
16. The Four Fourier Representations**

Exercises and Exploration

1. Exercises for Signals: The Basics**
2. Exercises for Sinusoidal Signals**
3. Explore Sinusoids**
4. Exercises for Exponentials, Steps, Impulses, and LTI System Properties**
5. Exercises for Impulse Response Descriptions for LTI Systems**
6. Explore Introduction to Linear Time-Invariant Systems**

Time Domain LTI Systems

1. Impulse Response and LTI Systems - Part II
2. Graphical Evaluation of Discrete-Time Convolution
3. Graphical Evaluation of Continuous-Time Convolution
4. Difference Equations: Solving System Responses with Stored Energy
5. Characteristics of Systems Described by Difference Equations**
6. Differential Equations: Solving System Responses with Stored Energy
7. Characteristics of Systems Described by Differential Equations
8. Two-Dimensional Signal Processing: Discrete Space

Exercises and Exploration

1. Exercises for Impulse Response and LTI Systems Part II
2. Exercises for Graphical Evaluation of Discrete-Time Convolution
3. Exercises for Graphical Evaluation of Continuous-Time Convolution
4. Exercises for Difference Equation Descriptions for Systems
5. Exercises for Differential Equation Descriptions for Systems
6. Explore Image Filtering

Fourier Series and Transforms

1. The Fourier Series: Continuous-Time Periodic Signals
2. Square Wave Fourier Series and the Sinc Function
3. Fourier Series Properties
4. The Fourier Transform:Linking Time and Frequency Domains**
5. Properties of the Fourier Transform
6. The Discrete-Time Fourier Transform**
7. Discrete-Time Fourier Transform Properties
8. Fourier Transforms and Discrete-Time Fourier Transforms for Periodic Signals
9. Frequency-Domain Descriptions for Continuous-Time Linear Time-Invariant Systems
10. Frequency-Domain Descriptions for Discrete-Time Linear Time-Invariant Systems**
11. Two-Dimensional Signal Processing: Continuous Space**

Sampling and Reconstruction

1. Introduction to Sampling and Reconstruction
2. Aliasing and the Sampling Theorem Simplified**
3. Fourier Transform Interpretation of Sampling**
4. Reconstruction and the Sampling Theorem
5. Reconstruction and the Sampling Theorem Examples
6. Two-Dimensional Sampling Theorem
7. Equivalent Analog Filtering
8. Practical Sampling: Anti-Aliasing Filters
9. Practical Reconstruction: The Zero-Order Hold
10. Practical Digital Filtering and Oversampling
11. Oversampling Example
12. Downsampling: Reducing the Sampling Rate
13. Upsampling: Increasing the Sampling Rate
14. Analog to Digital Conversion: Quantization and Coding
15. Analysis of Quantization Error

The DFT and Applications

1. Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform**
2. Important Discrete Fourier Transform Properties
3. Fast Fourier Transform (FFT) Algorithm**
4. Introduction to Circular Convolution and Filtering with the DFT
5. Circular Convolution Property of the Discrete Fourier Transform**
6. Filtering with the Discrete Fourier Transform
7. The Discrete Fourier Transform Approximation to the Fourier Transform
8. The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform
9. Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range
10. An Example of Approximating the Fourier Transform with the Discrete Fourier Transform
11. The Short-Time Fourier Transform and the Spectrogram
12. A Matrix Interpretation of the Discrete Fourier Transform
13. A Matrix Interpretation of the Fast Fourier Transform Algorithm

The $z$-Transform

1. Introduction to the z-Transform
2. The Region of Convergence for the z-Transform
3. Poles and Zeros of the z-Transform**
4. Properties of the Region of Convergence
5. Inversion of the z-Transform via Power Series Expansion
6. Inversion of the z-Transform: Partial Fraction Expansion
7. Properties of the z-Transform
8. z-Transform Analysis of LTI Systems
9. Stability and Causality of LTI Systems Described by Difference Equations
10. Inverse Systems for LTI Systems Described by Difference Equations
11. Minimum-Phase and All-Pass Systems
12. Frequency Response Magnitude and Poles and Zeros
13. Impulse Response and Poles and Zeros

Intro to Filter Design

1. Introduction to Frequency Selective Filtering
2. Characterizing Filter Phase Response
3. Zero-Phase Filtering
4. Overview of FIR and IIR Filters**

IIR Filter Design

1. IIR Filter Design Procedure
2. Analog Filters Used for IIR Filter Design
3. Continuous-Time Butterworth Filters
4. Continuous-Time Chebyshev and Elliptic Filters
5. Frequency Transformations for Continuous-Time Systems
6. The Bilinear Transform
7. IIR Filter Examples Designed Using MATLAB**
8. Poor IIR Filter Designs: Don't Make These Mistakes

FIR Filter Design

1. Introduction to FIR Filter Design
2. Frequency Sampling FIR Filter Design
3. Linear Phase FIR Filters
4. The Window Method of FIR Filter Design**
5. Parks-McClellan FIR Filter Design
6. Examples of Parks-McClellan FIR Filter Design

Part 2 - Professional level

Random Signal Characterization

1. Introduction to Random Signal Representations
2. Multivariable Random Signal Characterization
3. Random Processes and Stationarity
4. The Power Spectral Density
5. Cross Spectra and Coherence
6. LTI System Models for Random Signals
7. Autoregressive Models: The Yule-Walker Equations**

Basis Representation of Signals

1. Introduction to Signal Representation Using Bases
2. Introduction to Wavelets**
3. Multiresolution Analysis and the Scaling Function
4. Multiresolution Analysis and the Wavelet Decomposition
5. The Discrete Wavelet Transform
6. Wavelet Selection
7. Principal Component Analysis

Estimation of Power Spectra and Coherence

1. Parametric vs. Nonparametric Spectrum Estimation
2. The Periodogram
3. The Averaged Periodogram: Welch's Method**
4. Power Spectrum Estimation Examples: Welch's Method
5. Estimation of Coherence and Cross Spectra

Introduction to Signal Estimation and Detection Theory

1. Introduction to Estimation Theory
2. Parameter Estimation Criteria
3. Maximum Likelihood Estimation Examples
4. Introduction to Detection Theory
5. The Likelihood Ratio Test
6. The Generalized Likelihood Ratio Test

MMSE Filtering and Least-Squares Problems

1. Introduction to Minimum Mean-Squared Error Filtering**
2. Solving for the Minimum Mean-Squared Error Weights

Problems

1. Foundations**
2. Impulse Response Properties and Convolution
3. Difference- and Differential-Equation Descriptions for Systems
4. Review of Time-Domain Descriptions for Systems