The hyperbolic wavelet function

K. N. Le; K. P. Dabke; G. K. Egan

doi:10.1117/12.421221

The hyperbolic wavelet function

K. N. Le, K. P. Dabke, G. K. Egan

Monash University

Research output: Contribution to journal › Conference article › peer-review

10 Citations (Scopus)

Abstract

A survey of known wavelet groups is listed and properties of the symmetrical first-order hyperbolic wavelet function are studied. This new wavelet is the negative second derivative function of the hyperbolic kernel function, [sech(βθ)] where n = 1, 3, 5 ,... and n = 1 corresponds to the first-order hyperbolic kernel, which was recently proposed by the authors as a useful kernel for studying time-frequency power spectrum. Members of the "crude" wavelet group, which includes the hyperbolic, Mexican hat (Choi-Williams) and Morlet wavelets, are compared in terms of band-peak frequency, aliasing effects, scale limit, scale resolution and the total number of computed scales. The hyperbolic wavelet appears to have the finest scale resolution for well-chosen values of β ≤ 0.5 and the Morlet wavelet seems to have the largest total number of scales.

Original language	English
Pages (from-to)	411-422
Number of pages	12
Journal	Proceedings of SPIE: The International Society for Optical Engineering
Volume	4391
DOIs	https://doi.org/10.1117/12.421221
Publication status	Published - 2001
Externally published	Yes
Event	Wavelet Applications VIII - Orlando, FL, United States Duration: 18 Apr 2001 → 20 Apr 2001

Keywords

Aliasing
Hyperbolic wavelet
Mexican hat wavelet
Morlet wavelet
Scale resolution
Wavelet transform

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10.1117/12.421221

Cite this

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title = "The hyperbolic wavelet function",

abstract = "A survey of known wavelet groups is listed and properties of the symmetrical first-order hyperbolic wavelet function are studied. This new wavelet is the negative second derivative function of the hyperbolic kernel function, [sech(βθ)] where n = 1, 3, 5 ,... and n = 1 corresponds to the first-order hyperbolic kernel, which was recently proposed by the authors as a useful kernel for studying time-frequency power spectrum. Members of the {"}crude{"} wavelet group, which includes the hyperbolic, Mexican hat (Choi-Williams) and Morlet wavelets, are compared in terms of band-peak frequency, aliasing effects, scale limit, scale resolution and the total number of computed scales. The hyperbolic wavelet appears to have the finest scale resolution for well-chosen values of β ≤ 0.5 and the Morlet wavelet seems to have the largest total number of scales.",

keywords = "Aliasing, Hyperbolic wavelet, Mexican hat wavelet, Morlet wavelet, Scale resolution, Wavelet transform",

author = "Le, {K. N.} and Dabke, {K. P.} and Egan, {G. K.}",

year = "2001",

doi = "10.1117/12.421221",

language = "English",

volume = "4391",

pages = "411--422",

journal = "Proceedings of SPIE: The International Society for Optical Engineering",

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publisher = "SPIE",

note = "Wavelet Applications VIII ; Conference date: 18-04-2001 Through 20-04-2001",

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TY - JOUR

T1 - The hyperbolic wavelet function

AU - Le, K. N.

AU - Dabke, K. P.

AU - Egan, G. K.

PY - 2001

Y1 - 2001

N2 - A survey of known wavelet groups is listed and properties of the symmetrical first-order hyperbolic wavelet function are studied. This new wavelet is the negative second derivative function of the hyperbolic kernel function, [sech(βθ)] where n = 1, 3, 5 ,... and n = 1 corresponds to the first-order hyperbolic kernel, which was recently proposed by the authors as a useful kernel for studying time-frequency power spectrum. Members of the "crude" wavelet group, which includes the hyperbolic, Mexican hat (Choi-Williams) and Morlet wavelets, are compared in terms of band-peak frequency, aliasing effects, scale limit, scale resolution and the total number of computed scales. The hyperbolic wavelet appears to have the finest scale resolution for well-chosen values of β ≤ 0.5 and the Morlet wavelet seems to have the largest total number of scales.

AB - A survey of known wavelet groups is listed and properties of the symmetrical first-order hyperbolic wavelet function are studied. This new wavelet is the negative second derivative function of the hyperbolic kernel function, [sech(βθ)] where n = 1, 3, 5 ,... and n = 1 corresponds to the first-order hyperbolic kernel, which was recently proposed by the authors as a useful kernel for studying time-frequency power spectrum. Members of the "crude" wavelet group, which includes the hyperbolic, Mexican hat (Choi-Williams) and Morlet wavelets, are compared in terms of band-peak frequency, aliasing effects, scale limit, scale resolution and the total number of computed scales. The hyperbolic wavelet appears to have the finest scale resolution for well-chosen values of β ≤ 0.5 and the Morlet wavelet seems to have the largest total number of scales.

KW - Aliasing

KW - Hyperbolic wavelet

KW - Mexican hat wavelet

KW - Morlet wavelet

KW - Scale resolution

KW - Wavelet transform

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DO - 10.1117/12.421221

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VL - 4391

SP - 411

EP - 422

JO - Proceedings of SPIE: The International Society for Optical Engineering

JF - Proceedings of SPIE: The International Society for Optical Engineering

T2 - Wavelet Applications VIII

Y2 - 18 April 2001 through 20 April 2001

ER -

The hyperbolic wavelet function

Abstract

Keywords

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