Wavelet Transform Implementation for Vectors Using Lifting Scheme

This program implements wavelet transformation for vector data. Wavelet transform is a mathematical technique that decomposes signals into frequency components at different scales, enabling better understanding of signal characteristics. The implementation employs the Daubechies 9/7 wavelet function, which is realized through the lifting scheme method - an efficient algorithm that reduces computational complexity while maintaining transform quality. The lifting scheme implementation consists of three key stages: splitting, predicting, and updating. The algorithm processes input vectors through these stages to achieve multi-resolution analysis with perfect reconstruction properties. This approach allows effective handling of different frequency components within signals, making it particularly suitable for image compression and signal processing applications. By applying wavelet transformation, the program extracts detailed information about signal features across multiple scales, facilitating deeper analysis and processing of data. The implementation includes optimized functions for both forward and inverse transforms, ensuring computational efficiency while maintaining mathematical precision required for technical applications.