Implementation of Daubechies Wavelet Basis Construction

The primary objective of this program is to implement the construction of Daubechies wavelet bases. The implementation involves generating Daubechies wavelet basis functions through iterative filter bank algorithms and scaling function calculations, which are particularly valuable in signal processing and image processing applications. The program utilizes key mathematical operations including conjugate mirror filter design, polynomial factorization, and wavelet coefficient computation to achieve proper wavelet orthogonality and vanishing moment properties. Through this implementation, users can generate Daubechies wavelet basis functions at different scales and frequencies, enabling deeper understanding of wavelet transform principles and wavelet analysis applications. The code structure allows for parameter customization such as wavelet order (N) selection and decomposition level specification, facilitating research on wavelet characteristics across various scales. The modular design supports further enhancements for complex wavelet basis construction and transformation algorithms, including potential extensions to biorthogonal wavelets or adaptive wavelet schemes. The implementation provides comprehensive visualization capabilities for examining wavelet shape variations and frequency localization properties. Researchers can utilize this tool to explore wavelet applications in noise reduction, feature extraction, and multi-resolution analysis across different domains. The object-oriented architecture ensures easy integration with existing signal processing workflows while maintaining computational efficiency through optimized matrix operations and recursive algorithms. In summary, this program serves as a powerful foundation for both studying wavelet analysis theory and developing practical wavelet-based applications, with extensible code structure supporting future algorithmic improvements and specialized wavelet variants.