Discrete Wavelet Transform using Fractional Spline Wavelets 🌊

Welcome to the FrDWT repository! Here, you'll find a comprehensive collection of R functions to perform the Discrete Wavelet Transform (DWT) using fractional spline wavelets, covering both analysis and synthesis.

🔍 Overview

This repository includes:

• DWT Analysis & Synthesis: Functions to execute the Discrete Wavelet Transform using fractional spline wavelets.
• Plotting Tools: Visualize the levels of DWT, multiresolution analysis, and decomposition.
• Advanced Features:
  • Thresholding techniques
  • Wavelet confidence interval bootstrap
  • Wavelet scalogram and periodogram

There is a tutorial code serving as an example of how to perform Analysis and Syntesis using Fractional Spline Wavelets.

These R functions are based on the original MATLAB codes by Unser and Blu:

• Unser and Blu (1999)
• Unser and Blu (2000)
• Blu and Unser (2000)

These R codes were utilized in the following works:

• Pinto and Chiann (2023)
• Pinto and Chiann (2024)

Please ensure to cite these references when using the functions in this repository.

📑 References

1. Unser, M. & Blu, T. "Fractional splines and wavelets," SIAM Review, Vol. 42, No. 1, pp. 43–67, January 2000.
2. Unser, M. & Blu, T. "Construction of fractional spline wavelet bases," Proc. SPIE, Wavelet Applications in Signal and Image Processing VII, Denver, CO, USA, 19-23 July, 1999, vol. 3813, pp. 422-431.
3. Blu, T. & Unser, M. "The fractional spline wavelet transform: definition and implementation," Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'2000), Istanbul, Turkey, 5-9 June 2000, vol. I, pp. 512-515.
4. Pinto, M. G. de F. & Chiann, C. "Long-memory parameter estimation based on fractional spline wavelets," Digital Signal Processing, Vol. 133, March 2023, pp. 103836-1-12.
5. Pinto, M. G. de F. & Chiann, C. "A maximum-likelihood-based approach to estimate the long memory parameter using fractional spline wavelets," Signal Processing, Vol. 222, 2024, pp. 109518.

Feel free to explore the repository and reach out if you have any questions or need further assistance!