This repository focuses on the implementation and analysis of wavelet transforms for both one-dimensional (1D) and two-dimensional (2D) data. Wavelet analysis is a powerful tool for signal processing, data compression, and feature extraction, offering time-frequency localization and adaptability to non-stationary signals.
The repository includes implementations and results for various wavelets applied to simulated signals and images, enabling tasks such as noise reduction and cycle slip detection.
- Haar Wavelet
- Simple and efficient for basic signal processing tasks.
- Daubechies (D4, D6)
- Advanced wavelets offering better accuracy and multi-level decomposition.
- Mexican Hat Wavelet
- Ideal for edge detection and singularity analysis.
- Symlet Wavelet (S2)
- A symmetric variant of Daubechies wavelets for improved signal reconstruction.
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Noise Reduction
Using wavelets to filter out noise from 1D signals while retaining essential features. -
Cycle Slip Detection in GNSS Signals
Applying wavelets to identify and detect discontinuities in GPS signals. -
2D Image Denoising
Enhancing image quality by removing Salt & Pepper and Gaussian noise.
- Noise reduction results demonstrate significant improvements with Daubechies6 Wavelet at level 2 decomposition, yielding the least error in signal reconstruction.
- Visualizations of denoised images highlight the effectiveness of different wavelets, with comparative performance metrics available in the results section.