Wavelet Transform Tutorial

A hands-on MATLAB tutorial introducing the fundamentals and practical application of wavelet transforms for signal and image analysis.

This repository accompanies a series of tutorial exercises that guide students through:

• Understanding the theory behind wavelet transforms
• Performing multi-resolution signal analysis
• Applying discrete wavelet transforms (DWT)
• Visualizing time-frequency representations
• Exploring wavelet-based denoising and feature extraction
• Working with real-world data examples

Repository Structure

waveletTransform_tutorial/
│
├── code/                    # Tutorial scripts and example solutions
├── data/                    # Example datasets used throughout the exercises
├── functions/               # Helper functions for wavelet analysis
│
├── Tutorial_IIA_instructions.pdf
├── Tutorial_IIB_instructions.pdf
├── Tutorial_IIC_instructions.pdf
│
└── README.md

Prerequisites

MATLAB

The tutorials were developed using MATLAB.

Recommended MATLAB toolboxes:

• Wavelet Toolbox
• Signal Processing Toolbox

Getting Started

1. Clone the repository:

git clone https://github.com/stefan-ehrlich/waveletTransform_tutorial.git
cd waveletTransform_tutorial

2. Open MATLAB.

3. Add the repository to your MATLAB path:

addpath(genpath(pwd));

4. Open the tutorial instructions:

• Tutorial_IIA_instructions.pdf
• Tutorial_IIB_instructions.pdf
• Tutorial_IIC_instructions.pdf

5. Follow the exercises in sequence.

Tutorial Overview

Tutorial IIA – Fundamentals of Wavelets

Topics include:

• Fourier transform limitations
• Time-frequency analysis
• Wavelet concepts
• Scaling and translation
• Mother wavelets

Tutorial IIB – Discrete Wavelet Transform

Topics include:

• Filter banks
• Multi-level decomposition
• Approximation and detail coefficients
• Signal reconstruction

Tutorial IIC – Applications

Topics include:

• Signal denoising
• Compression
• Feature extraction
• Biomedical signal analysis

Example Workflow

% Load example data
load('data/example_signal.mat')

% Perform wavelet decomposition
[c,l] = wavedec(signal,4,'db4');

% Visualize coefficients
plot(c)

% Reconstruct approximation
approx = wrcoef('a',c,l,'db4',4);

Learning Objectives

After completing the tutorials, participants should be able to:

• Explain the motivation behind wavelet transforms
• Distinguish between Fourier and wavelet analysis
• Perform wavelet decomposition and reconstruction
• Interpret wavelet coefficients
• Apply wavelet methods to practical data analysis problems

References

Recommended reading:

1. Cohen, M. X. (2014). Analyzing neural time series data: theory and practice. MIT press.
2. Mallat, S. A Wavelet Tour of Signal Processing.
3. Daubechies, I. Ten Lectures on Wavelets.
4. MATLAB Wavelet Toolbox Documentation.

License

Please refer to the repository license information before redistribution or modification.

Author

Stefan Ehrlich GitHub: https://github.com/stefan-ehrlich