On the relationship between 1/f and /spl alpha/-stable processes

Jijun Yin; Athina P. Petropulu

doi:https://doi.org/10.1109/ICASSP.1998.681755

On the relationship between 1/f and /spl alpha/-stable processes

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

1/f/sup /spl beta//-type spectral behavior has received considerable attention in the past few years because it arises from a wide range of natural phenomena. By expressing a 1/f/sup /spl beta// process as a fractional integral of white noise, we show that, if /spl beta/1, the process has stationary /spl alpha/-stable increments. We also provide closed form expressions for the relationship between /spl beta/ and /spl alpha/. The theoretical results are verified via real ultrasound data. Ultrasound breast data, or their increments, which appear to be 1/f/sup /spl beta//, are shown to follow reasonably well the /spl alpha/-stable model.

Original language	American English
Title of host publication	Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1585-1588
Number of pages	4
ISBN (Print)	0780344286, 9780780344280
DOIs	https://doi.org/10.1109/ICASSP.1998.681755
State	Published - 1998
Externally published	Yes
Event	1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998 - Seattle, WA, United States Duration: May 12 1998 → May 15 1998

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	3

Other

Other	1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998
Country/Territory	United States
City	Seattle, WA
Period	5/12/98 → 5/15/98

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering

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https://doi.org/10.1109/ICASSP.1998.681755

Cite this

Yin, J., & Petropulu, A. P. (1998). On the relationship between 1/f and /spl alpha/-stable processes. In Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998 (pp. 1585-1588). [681755] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 3). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.1998.681755

Yin, Jijun ; Petropulu, Athina P. / On the relationship between 1/f and /spl alpha/-stable processes. Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998. Institute of Electrical and Electronics Engineers Inc., 1998. pp. 1585-1588 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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abstract = "1/f/sup /spl beta//-type spectral behavior has received considerable attention in the past few years because it arises from a wide range of natural phenomena. By expressing a 1/f/sup /spl beta// process as a fractional integral of white noise, we show that, if /spl beta/1, the process has stationary /spl alpha/-stable increments. We also provide closed form expressions for the relationship between /spl beta/ and /spl alpha/. The theoretical results are verified via real ultrasound data. Ultrasound breast data, or their increments, which appear to be 1/f/sup /spl beta//, are shown to follow reasonably well the /spl alpha/-stable model.",

author = "Jijun Yin and Petropulu, {Athina P.}",

year = "1998",

doi = "https://doi.org/10.1109/ICASSP.1998.681755",

language = "American English",

isbn = "0780344286",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

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pages = "1585--1588",

booktitle = "Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998",

address = "United States",

note = "1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998 ; Conference date: 12-05-1998 Through 15-05-1998",

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Yin, J & Petropulu, AP 1998, On the relationship between 1/f and /spl alpha/-stable processes. in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998., 681755, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 3, Institute of Electrical and Electronics Engineers Inc., pp. 1585-1588, 1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998, Seattle, WA, United States, 5/12/98. https://doi.org/10.1109/ICASSP.1998.681755

On the relationship between 1/f and /spl alpha/-stable processes. / Yin, Jijun; Petropulu, Athina P.
Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998. Institute of Electrical and Electronics Engineers Inc., 1998. p. 1585-1588 681755 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

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AU - Petropulu, Athina P.

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AB - 1/f/sup /spl beta//-type spectral behavior has received considerable attention in the past few years because it arises from a wide range of natural phenomena. By expressing a 1/f/sup /spl beta// process as a fractional integral of white noise, we show that, if /spl beta/1, the process has stationary /spl alpha/-stable increments. We also provide closed form expressions for the relationship between /spl beta/ and /spl alpha/. The theoretical results are verified via real ultrasound data. Ultrasound breast data, or their increments, which appear to be 1/f/sup /spl beta//, are shown to follow reasonably well the /spl alpha/-stable model.

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M3 - Conference contribution

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T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

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BT - Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998

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Yin J, Petropulu AP. On the relationship between 1/f and /spl alpha/-stable processes. In Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998. Institute of Electrical and Electronics Engineers Inc. 1998. p. 1585-1588. 681755. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: https://doi.org/10.1109/ICASSP.1998.681755

On the relationship between 1/f and /spl alpha/-stable processes

Abstract

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