傅立叶特征函数,不确定Gabor原理和等分辨小波

L. R. Soares, Hélio M. de Oliveira, R. Cintra, R. Souza
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引用次数: 17

摘要

研究傅里叶变换下的形状不变信号,得到傅里叶算子的一类特征函数。对经典的测不准原理加伯-海森堡原理进行了重新研究,并引入了联合时频分析中的等分辨概念。结果表明,任何傅里叶特征函数都能达到等分辨率。结果表明,通过适当的尺度变换,每个已知的小波族都可以得到一个等分辨率小波。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.
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