离散分数阶傅里叶变换交换矩阵方法的比较研究

I. Bhatta, Balu Santhanam
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引用次数: 8

摘要

分数阶傅里叶变换作为传统傅里叶变换的扩展和一种时频信号分析工具,适用于处理各种类型的非平稳信号。离散分数阶傅里叶变换(DFRFT)的计算及其啁啾集中特性都依赖于计算中使用的DFT特征向量的基础。已经提出了几种用于变换计算的dft特征向量基,但没有一个通用的框架来比较它们。在本文中,我们从概念的角度比较几种不同的方法,并回顾它们之间的差异。讨论了五种不同的求中心- dft (CDFT)交换矩阵的方法以及这些交换矩阵的各种性质。我们研究了这些交换矩阵的特征值和特征向量的性质,以确定它们是否与相应的连续高斯-埃尔米算子相似。我们还从以下几个方面衡量了这五种方法的性能:信副瓣比、10db带宽、质量因子、特征值的线性度、啁啾参数估计误差,以及最后的峰参数映射区域。我们比较了使用这些性能指标的五种方法,并指出改进的QMFD方法在啁啾频谱峰带宽、峰参数映射的可逆性、特征值谱的线性和啁啾参数估计误差方面产生了最好的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A comparative study of commuting matrix approaches for the discrete fractional fourier transform
As an extension of the conventional Fourier transform and as a time-frequency signal analysis tool, the fractional Fourier transforms (FRFT) are suitable for dealing with various types of non-stationary signals. Computation of the discrete fractional Fourier transform (DFRFT) and its chirp concentration properties are both dependent on the basis of DFT eigenvectors used in the computation. Several DFT-eigenvector bases have been proposed for the computation of transform, and there is no common framework for comparing them. In this paper, we compare several different approaches from a conceptual viewpoint and review the differences between them. We discuss five different approaches to find centered-DFT (CDFT) commuting matrices and the various properties of these commuting matrices. We study the properties of the eigenvalues and eigenvectors of these commuting matrices to determine whether they resemble those of corresponding continuous Gauss-Hermite operator. We also measure the performance of these five approaches in terms of: mailobe-to-sidelobe ratio, 10-dB bandwidth, quality factor, linearity of eigenvalues, chirp parameter estimation error, and, finally the peak-to-parameter mapping regions. We compare the five approaches using these performance metrics and point out that the modified QMFD approach produces the best results in terms of bandwidth of the spectral peak for a chirp, invertibility of the peak-parameter mapping, linearity of the eigenvalue spectrum and chirp parameter estimation errors.
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