This example curriculum is focussed on the methods and techniques for estimating spectra from data.
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
LTI Systems and Fourier Transforms
These lessons may be omitted if you have a background in signals and systems.
- Impulse Response and LTI Systems - Part II
- The Fourier Transform:Linking Time and Frequency Domains
- Properties of the Fourier Transform
- The Discrete-Time Fourier Transform
- Discrete-Time Fourier Transform Properties
Sampling and Reconstruction
- Introduction to Sampling and Reconstruction
- Aliasing and the Sampling Theorem Simplified
- Practical Sampling: Anti-Aliasing Filters
The DFT and Applications
- Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform
- Important Discrete Fourier Transform Properties
- Fast Fourier Transform (FFT) Algorithm
- 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
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
