wavelet-signal-processing-thesis

A comprehensive Bachelor's graduation project exploring wavelet transforms, their mathematical foundations, and real-world applications in signal and image processing using Python.

Wavelet Transform and Its Applications

This is my Bachelor of Science graduation project titled "Wavelet Transform and Its Applications", submitted to the Department of Mathematics, Faculty of Science, Damietta University, Class of 2025.

📚 Summary

This project explores:

• The mathematical foundations of signal processing:
  • Convolution
  • Fourier Series and Fourier Transform
  • STFT (Short-Time Fourier Transform)
  • Gabor Transform
  • Wavelet Theory (Continuous and Discrete)
• A focus on Haar wavelets and multiresolution analysis
• Python implementations using NumPy, Matplotlib, and PyWavelets
• Applications in:
  • Image compression
  • Signal denoising
  • Frequency analysis

🧪 Technologies

• Python
• PyWavelets (pywt)
• NumPy
• Matplotlib

📁 Structure

• 📜 Wavelets_Bachelor_Thesis.pdf – Full PDF of the thesis
• 🖼️ haar_dwt_demo.py – Image decomposition using Haar DWT
• 📦 fourier_compression.py – Frequency-based image compression
• 🎯 wavelet_vs_stft.py – Time-frequency analysis comparison

🎯 Future Work

This project is a base for potential research into:

• Wavelet-based CNNs
• Real-time signal processing
• Medical image analysis using advanced wavelet families

👥 Authors

• Ezzelddin Wael Wafik Megahead
• Ahmed Mohammed Hashem

🎓 Supervisor

• Dr. Abdelhamid Badran