A Data Representation Based on Block Wavelet Transform in Modified Form

Abstract

The main idea of wavelet transform is to analyze a function at different scales. The transform results depend on how much it matches the function being analyzed. Wavelets at different resolutions produce different results. It's most important for the transform in block form, when execution is based on a source data fragments. Execution variants of block wavelet transform are considered. There are forms depending on the processing direction and invariant to it. A mathematical description is proposed in matrix form. The division of space-frequency plane for various processing options is presented for a one-dimensional signal. All main variants are considered. The transform results for the corresponding forms are shown.