论文标题
与线性典型变换相关的非均匀多解析分析
Nonuniform Multiresolution Analysis Associated with Linear Canonical Transform
论文作者
论文摘要
线性规范变换（LCT）在短时间内已达到可观的地位，并且在科学和工程的几个学科中广泛使用，包括信号处理，光学和雷达系统，电气和通信系统，量子物理学等，这主要是由于额外的自由度以及简单的几何表现。在本文中，我们在频谱上介绍了一项新颖的多解决分析（LCT-numra），$ω= \ big \ {0，{r}/{n}/{n} \ big \}+2 \ mathbb {z}，$ n $ n \ geqq Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q QQ1 $ $ r $和$ n $是相对典型的，通过缠绕不均匀MRA和线性规范变换的想法。我们首先开发与LCT相关的非均匀多分辨率分析，然后驱动算法从线性规范的低通滤波器$λ_{0}^{M}（ω）$从适当条件下构建LCT-numra。然而，为了扩展本研究的范围，我们为这种MRA构造了相关的小波包，并通过线性规范变换来研究它们的性质。
The linear canonical transform (LCT) has attained respectable status within a short span and is being broadly employed across several disciplines of science and engineering including signal processing, optical and radar systems, electrical and communication systems, quantum physics etc, mainly due to the extra degrees of freedom and simple geometrical manifestation. In this article, we introduce a novel multiresolution analysis (LCT-NUMRA) on the spectrum $Ω= \big\{0,{r}/{N}\big\}+2\mathbb{Z},$ where $N \geqq 1$ is an integer and $r$ is an odd integer with $ 1 \leqq r \leqq 2N-1,$ such that $r$ and $N$ are relatively prime, by intertwining the ideas of nonuniform MRA and linear canonical transforms. We first develop nonuniform multiresolution analysis associated with the LCT and then drive an algorithm to construct an LCT-NUMRA starting from a linear canonical low-pass filter $Λ_{0}^{M}(ω)$ with suitable conditions. Nevertheless, to extend the scope of the present study, we construct the associated wavelet packets for such an MRA and investigate their properties by means of the linear canonical transforms.
