@article{82a9d1c991674231a6ddf10b25fff367,
title = "A Pseudo-Bertrand distribution for time-scale analysis",
abstract = "Using the pseudo-Wigner time-frequency distribution as a guide, we derive two new time-scale representations: the pseudo-Bertrand and the smoothed pseudo-Bertrand distributions. Unlike the Bertrand distribution, these representations support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the affine smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components.",
author = "Paulo Con{\c c}alv{\'e}s and Baraniuk, {Richard G.}",
note = "Funding Information: Manuscript received July 18, 1995 This work was supported by the Na- tional Science Foundatlon under Grant MIP-9457438, by the Office of Naval Research under Grant N00014-95-1-0849, and by the State of Texas Advanced Technology Program under Grant TX-ATP 003604-002 The associate editor coordinating the review of this paper and approving it for pubhcatlon was Prof A Tewfik alv6s is with the Department of Electncal and Computer Engmeer-University, Houston, TX 77251-1892 USA, on leave from Ecole Normale Sup&{"} de Lyon, Lyon, France. R Baraniuk is with the Department of Electncal and Computer Engmeenng, Rice University, Houston, TX 77251-1892 USA Publisher Item Identifier S 1070-9908(96)02740-X. 'Throughout this paper, we will employ the followmg notation: The variables t and f correspond to time and frequency, respectively; all integrals run from --oo to fw,lo wer-case letters denote tune funchons, and upper- case letters denote Fourier transforms We will also consider only analytic signals, where X ( f ) E 0 V f < 0 Usually, the wavelet transform is expressed as a function of a time vanable t and a scale vanahle a. Here, we will use the reparametmation of scale as inverse frequency a = fo / f suggested in [2] and assume, without loss of generahty, that the center frequency fo of the wavelet $ equals 1 Hz This interpretation of scale should not be confused with that of Cohen [4]",
year = "1996",
month = mar,
doi = "10.1109/97.481162",
language = "English (US)",
volume = "3",
pages = "82--84",
journal = "IEEE Signal Processing Letters",
issn = "1070-9908",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",
}