Notation, Symbols, and Abbreviations
How to Learn Signal Processing with allsignalprocessing.com
Signal Processing Curricula - Unlimited Possibilities
allsignalprocessing.com Blog
allsignalprocessing.com Lessons
** denotes lessons available with introductory membership
Part 1
Essentials and Professional levels
Foundations
- Signals Everywhere**
- Ever-Present Noise**
- Models, Math, and Real-World Signals**
- Four Signal-Processing Themes**
- Building Signals with Blocks: Basis Expansions**
- Signals: The Basics**
- Sinusoidal Signals**
- Sinusoidal Signals Examples**
- Complex Sinusoids**
- Exponential, Step, and Impulse Signals**
- Introduction to Linear, Time-Invariant Systems**
- Introduction to Difference Equation System Descriptions**
- Impulse Response Descriptions for LTI Systems**
- Frequency Response Descriptions for LTI Systems**
- Introduction to the System Function and System Poles and Zeros**
- The Four Fourier Representations**
Exercises and Exploration
- Exercises for Signals: The Basics**
- Exercises for Sinusoidal Signals**
- Explore Sinusoids**
- Exercises for Exponentials, Steps, Impulses, and LTI System Properties**
- Exercises for Impulse Response Descriptions for LTI Systems**
- Explore Introduction to Linear Time-Invariant Systems**
Time Domain LTI Systems
- Impulse Response and LTI Systems - Part II
- Graphical Evaluation of Discrete-Time Convolution
- Graphical Evaluation of Continuous-Time Convolution
- Difference Equations: Solving System Responses with Stored Energy
- Characteristics of Systems Described by Difference Equations**
- Differential Equations: Solving System Responses with Stored Energy
- Characteristics of Systems Described by Differential Equations
- Two-Dimensional Signal Processing: Discrete Space
Exercises and Exploration
- Exercises for Impulse Response and LTI Systems Part II
- Exercises for Graphical Evaluation of Discrete-Time Convolution
- Exercises for Graphical Evaluation of Continuous-Time Convolution
- Exercises for Difference Equation Descriptions for Systems
- Exercises for Differential Equation Descriptions for Systems
- Explore Image Filtering
Fourier Series and Transforms
- The Fourier Series: Continuous-Time Periodic Signals
- Square Wave Fourier Series and the Sinc Function
- Fourier Series Properties
- The Fourier Transform:Linking Time and Frequency Domains**
- Properties of the Fourier Transform
- The Discrete-Time Fourier Transform**
- Discrete-Time Fourier Transform Properties
- Fourier Transforms and Discrete-Time Fourier Transforms for Periodic Signals
- Frequency-Domain Descriptions for Continuous-Time Linear Time-Invariant Systems
- Frequency-Domain Descriptions for Discrete-Time Linear Time-Invariant Systems**
- Two-Dimensional Signal Processing: Continuous Space**
Sampling and Reconstruction
- Introduction to Sampling and Reconstruction
- Aliasing and the Sampling Theorem Simplified**
- Fourier Transform Interpretation of Sampling**
- Reconstruction and the Sampling Theorem
- Reconstruction and the Sampling Theorem Examples
- Two-Dimensional Sampling Theorem
- Equivalent Analog Filtering
- Practical Sampling: Anti-Aliasing Filters
- Practical Reconstruction: The Zero-Order Hold
- Practical Digital Filtering and Oversampling
- Oversampling Example
- Downsampling: Reducing the Sampling Rate
- Upsampling: Increasing the Sampling Rate
- Analog to Digital Conversion: Quantization and Coding
- Analysis of Quantization Error
The DFT and Applications
- Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform**
- Important Discrete Fourier Transform Properties
- Fast Fourier Transform (FFT) Algorithm**
- Introduction to Circular Convolution and Filtering with the DFT
- Circular Convolution Property of the Discrete Fourier Transform**
- Filtering with the Discrete Fourier Transform
- The Discrete Fourier Transform Approximation to the Fourier Transform
- The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform
- Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range
- An Example of Approximating the Fourier Transform with the Discrete Fourier Transform
- The Short-Time Fourier Transform and the Spectrogram
- A Matrix Interpretation of the Discrete Fourier Transform
- A Matrix Interpretation of the Fast Fourier Transform Algorithm
The
-Transform
- Introduction to the z-Transform
- The Region of Convergence for the z-Transform
- Poles and Zeros of the z-Transform**
- Properties of the Region of Convergence
- Inversion of the z-Transform via Power Series Expansion
- Inversion of the z-Transform: Partial Fraction Expansion
- Properties of the z-Transform
- z-Transform Analysis of LTI Systems
- Stability and Causality of LTI Systems Described by Difference Equations
- Inverse Systems for LTI Systems Described by Difference Equations
- Minimum-Phase and All-Pass Systems
- Frequency Response Magnitude and Poles and Zeros
- Impulse Response and Poles and Zeros
Intro to Filter Design
- Introduction to Frequency Selective Filtering
- Characterizing Filter Phase Response
- Zero-Phase Filtering
- Overview of FIR and IIR Filters**
IIR Filter Design
- IIR Filter Design Procedure
- Analog Filters Used for IIR Filter Design
- Continuous-Time Butterworth Filters
- Continuous-Time Chebyshev and Elliptic Filters
- Frequency Transformations for Continuous-Time Systems
- The Bilinear Transform
- IIR Filter Examples Designed Using MATLAB**
- Poor IIR Filter Designs: Don't Make These Mistakes
FIR Filter Design
- Introduction to FIR Filter Design
- Frequency Sampling FIR Filter Design
- Linear Phase FIR Filters
- The Window Method of FIR Filter Design**
- Parks-McClellan FIR Filter Design
- Examples of Parks-McClellan FIR Filter Design
Part 2 - Professional level
Random Signal Characterization
- Introduction to Random Signal Representations
- Multivariable Random Signal Characterization
- Random Processes and Stationarity
- The Power Spectral Density
- Cross Spectra and Coherence
- LTI System Models for Random Signals
- Autoregressive Models: The Yule-Walker Equations**
Basis Representation of Signals
- Introduction to Signal Representation Using Bases
- Introduction to Wavelets**
- Multiresolution Analysis and the Scaling Function
- Multiresolution Analysis and the Wavelet Decomposition
- The Discrete Wavelet Transform
- Wavelet Selection
- Principal Component Analysis
Estimation of Power Spectra and Coherence
- Parametric vs. Nonparametric Spectrum Estimation
- The Periodogram
- The Averaged Periodogram: Welch's Method**
- Power Spectrum Estimation Examples: Welch's Method
- Estimation of Coherence and Cross Spectra
Introduction to Signal Estimation and Detection Theory
- Introduction to Estimation Theory
- Parameter Estimation Criteria
- Maximum Likelihood Estimation Examples
- Introduction to Detection Theory
- The Likelihood Ratio Test
- The Generalized Likelihood Ratio Test
MMSE Filtering and Least-Squares Problems
- Introduction to Minimum Mean-Squared Error Filtering**
- Solving for the Minimum Mean-Squared Error Weights