Foundations
- Signals Everywhere - Free Lesson
- Ever-Present Noise - Free Lesson
- Models, Math, and Real-World Signals - Free Lesson
- Four Signal-Processing Themes - Free Lesson
- Jupyter Notebook: Explore FIR Filtering - Free Lesson
- Jupyter Notebook: Explore Image Filtering - Free Lesson
- Building Signals with Blocks: Basis Expansions - Free Lesson
- Signals: The Basics - Free Lesson
- Sinusoidal Signals - Free Lesson
- Sinusoidal Signals Examples - Free Lesson
- Complex Sinusoids - Free Lesson
- Exponential, Step, and Impulse Signals - Free Lesson
- Introduction to Linear, Time-Invariant Systems - Free Lesson
- Introduction to Difference Equation System Descriptions - Free Lesson
- Impulse Response Descriptions for LTI Systems - Free Lesson
- Frequency Response Descriptions for LTI Systems - Free Lesson
- Introduction to the System Function and System Poles and Zeros - Free Lesson
- The Four Fourier Representations - Free Lesson
- Summary Problems for Foundations - Free Lesson
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 - Free Lesson
- Differential Equations: Solving System Responses with Stored Energy
- Characteristics of Systems Described by Differential Equations
- Two-Dimensional Signal Processing: Discrete Space
- Problems for Time Domain LTI Systems
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 - Free Lesson
- Properties of the Fourier Transform
- The Discrete-Time Fourier Transform - Free Lesson
- 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 - Free Lesson
- Fourier Transform Interpretation of Sampling - Free Lesson
- 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 - Free Lesson
- Important Discrete Fourier Transform Properties
- Fast Fourier Transform (FFT) Algorithm - Free Lesson
- Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform
- 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
- Jupyter Notebook: Explore the Windowed DFT
- An Example of Approximating the Fourier Transform with the Discrete Fourier Transform
- The Short-Time Fourier Transform and the Spectrogram
- Jupyter Notebook: Explore the Spectrogram
- A Matrix Interpretation of the Discrete Fourier Transform
- A Matrix Interpretation of the Fast Fourier Transform Algorithm
The Z-Transform
- Minimum-Phase and All-Pass Systems
- Frequency Response Magnitude and Poles and Zeros
- Impulse Response and Poles and Zeros
- Inversion of the
-Transform: Partial Fraction Expansion - Properties of the -Transform
- -Transform Analysis of LTI Systems
- Stability and Causality of LTI Systems Described by Difference Equations
- Inverse Systems for LTI Systems Described by Difference Equations
- Introduction to the -Transform
- The Region of Convergence for the -Transform
- Poles and Zeros of the -Transform - Free Lesson
- Properties of the Region of Convergence
- Inversion of the -Transform via Power Series Expansion
Intro to Filter Design
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 - Free Lesson
- Poor IIR Filter Designs: Don't Make These Mistakes
- Jupyter Notebook: IIR Filter Design Examples
