Time-frequency transforms of white noises and Gaussian analytic functions
نویسندگان
چکیده
A family of Gaussian analytic functions (GAFs) has recently been linked to the Gabor transform white noises [4]. This answered pioneering work by Flandrin [10], who observed that zeros noise had a regular distribution and proposed filtering algorithms based on spectrogram. In this paper, we study in systematic way link between GAFs class time-frequency transforms noises. Our main observation is correspondence pairs (transform, GAF) generating for classical orthogonal polynomials. covers some transforms, such as Daubechies-Paul wavelet transform. It also unveils new windowed discrete Fourier which map fundamental GAFs. Moreover, discuss subtleties defining its infinite dimensional Hilbert spaces finite approximations.
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2021
ISSN: ['1096-603X', '1063-5203']
DOI: https://doi.org/10.1016/j.acha.2019.07.003