Implementation of Second Generation Wavelet Transform Using Lifting Scheme

This paper presents a program that implements second-generation wavelet transform using fractional-order wavelet transform through the lifting scheme. The implementation operates in the time domain and follows a column-first then row-second processing sequence. The fractional-order wavelet transform, based on the lifting scheme, enhances the effectiveness of wavelet transformation by providing more flexible frequency localization. This method plays a significant role in signal processing and image processing applications, enabling more precise analysis and processing of signals and images through improved adaptation to signal characteristics. The implementation typically involves three main stages: splitting the signal into even and odd samples, predicting odd samples from even ones using prediction filters, and updating even samples using update filters. The fractional-order aspect allows for non-integer scaling factors, providing finer control over frequency resolution. The column-row processing sequence ensures efficient 2D signal handling by first processing columns then rows, which is particularly beneficial for image processing applications where wavelet coefficients need to be computed efficiently across both dimensions.