Automation of the lifting factorisation of wavelet transforms

Abstract
Wavelets are sets of basis functions used in the analysis of signals and images. In contrast to Fourier analysis, wavelets have both spatial and frequency localization, making them useful for the analysis of sharply-varying or non-periodic signals. The lifting scheme for finding the discrete wavelet transform was demonstrated by Daubechies and Sweldens (1996). In particular, they showed that this method depends on the factorization of polyphase matrices, whose entries are Laurent polynomials,...

Title of program: LiftingFactorisation.nb 1.0
Catalogue Id: ADLE_v1_0

Nature of problem
Spectral analysis and compression of signals or images.

Versions of this program held in the CPC repository in Mendeley Data
ADLE_v1_0; LiftingFactorisation.nb 1.0; 10.1016/S0010-4655(99)00451-8

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
小波（Wavelets）是一类用于信号与图像分析的基函数集合。相较于傅里叶分析（Fourier analysis），小波兼具空间与频率局域化特性，使其可有效分析剧烈变化或非周期性信号。1996年，道布奇（Daubechies）与斯韦尔登斯（Sweldens）提出了离散小波变换（discrete wavelet transform）的提升格式（lifting scheme）。他们特别证明，该方法依赖于多相位矩阵（polyphase matrices）的因式分解，这类矩阵的元素为洛朗多项式（Laurent polynomials）……

程序名称：LiftingFactorisation.nb 1.0
目录编号：ADLE_v1_0

问题本质
信号或图像的频谱分析与压缩。

本程序在曼德利数据（Mendeley Data）的CPC仓库中的版本
ADLE_v1_0; LiftingFactorisation.nb 1.0; 10.1016/S0010-4655(99)00451-8

本程序源自贝尔法斯特女王大学所藏的CPC程序库（1969-2019年）。