Mexican Hat Wavelet Transform Source Code

This is the complete source code for Mexican Hat Wavelet Transform, developed in MATLAB environment. The Mexican Hat Wavelet Transform is a powerful signal processing technique used for signal analysis and processing. The core implementation involves convolving the input signal with the Mexican Hat wavelet function, which is defined mathematically as the second derivative of the Gaussian function. The characteristic shape of this wavelet resembles a Mexican sombrero, hence its name. Key implementation features include: - Wavelet scaling and translation operations - Convolution algorithms for efficient signal processing - Frequency domain analysis capabilities - Multi-resolution signal decomposition The transform finds extensive applications across various domains including image processing (edge detection, feature extraction), speech processing (pitch detection, formant analysis), and biomedical engineering (ECG signal analysis, medical imaging). This implementation provides a robust foundation for wavelet-based signal analysis with configurable parameters for scale selection and resolution control. The source code includes main functions for: 1. Wavelet generation using the mathematical formula: ψ(t) = (1-t²)·e^(-t²/2) 2. Signal convolution methods with optimized computational efficiency 3. Scale-space representation visualization 4. Inverse transform capabilities for signal reconstruction This codebase serves as a comprehensive reference for researchers and engineers working with wavelet transforms, offering both educational value and practical implementation ready for integration into larger signal processing systems.