This example curriculum focusses on filtering data and design of frequency-selective filters.
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
- Fourier Transform Interpretation of Sampling
- Reconstruction and the Sampling Theorem
- Reconstruction and the Sampling Theorem Examples
- 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 zz-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
- 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
Option 1 requires minimal understanding of continuous-time systems theory. For more detail on the analog filters used in IIR filter design, choose Option 2 instead of Option 1. Option 3 presents the theory underlying MATLAB's approach to IIR filter design and can be omitted for a less mathematical treatment.
- IIR Filter Design Procedure
- Option 1: Analog Filters Used for IIR Filter Design
- Option 2: Continuous-Time Butterworth Filters
- Option 2: Continuous-Time Chebyshev and Elliptic Filters
- Option 3: Frequency Transformations for Continuous-Time Systems
- Option 3: The Bilinear Transform
- IIR Filter Examples Designed Using MATLAB
- Poor IIR Filter Designs: Don't Make These Mistakes
FIR Filter Design
The Parks-McClellan approach to FIR filter design is by far the most powerful and useful.
