Signal concentration on unit sphere: A local K-th moment zenithal energy concentration measure

Liying Wei; Rodney A. Kennedy; Tharaka A. Lamahewa

doi:10.1109/AUSCTW.2010.5426775

Signal concentration on unit sphere: A local K-th moment zenithal energy concentration measure

Liying Wei^*, Rodney A. Kennedy, Tharaka A. Lamahewa

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We define a k-th moment zenithal energy concentration measure for a polar cap region on the unit sphere. The optimal functions are obtained with the maximal local k-th moment zenithal measure (LMZM). Compared to the spherical Slepian function in the cap region and the optimal function with the minimal global k-th moment zenithal measure (GMZM), we show that: 1) as k increases, the tail of the function with LMZM decays more quickly; 2) the main lobe of the optimal function with LMZM moves as the maximum colatitude of the cap increases; while the spherical Slepian function does not change much and the function with GMZM is by definition invariant; and 3) LMZM has no obvious advantage over the spherical Slepian function and the GMZM optimal function in both the energy concentration and tail decay rate.

Original language	English
Title of host publication	2010 Australian Communications Theory Workshop, AusCTW 2010
Pages	97-101
Number of pages	5
DOIs	https://doi.org/10.1109/AUSCTW.2010.5426775
Publication status	Published - 2010
Event	2010 Australian Communications Theory Workshop, AusCTW 2010 - Canberra, ACT, Australia Duration: 3 Feb 2010 → 5 Feb 2010

Publication series

Name	2010 Australian Communications Theory Workshop, AusCTW 2010

Conference

Conference	2010 Australian Communications Theory Workshop, AusCTW 2010
Country/Territory	Australia
City	Canberra, ACT
Period	3/02/10 → 5/02/10

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10.1109/AUSCTW.2010.5426775

Cite this

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title = "Signal concentration on unit sphere: A local K-th moment zenithal energy concentration measure",

abstract = "We define a k-th moment zenithal energy concentration measure for a polar cap region on the unit sphere. The optimal functions are obtained with the maximal local k-th moment zenithal measure (LMZM). Compared to the spherical Slepian function in the cap region and the optimal function with the minimal global k-th moment zenithal measure (GMZM), we show that: 1) as k increases, the tail of the function with LMZM decays more quickly; 2) the main lobe of the optimal function with LMZM moves as the maximum colatitude of the cap increases; while the spherical Slepian function does not change much and the function with GMZM is by definition invariant; and 3) LMZM has no obvious advantage over the spherical Slepian function and the GMZM optimal function in both the energy concentration and tail decay rate.",

author = "Liying Wei and Kennedy, {Rodney A.} and Lamahewa, {Tharaka A.}",

year = "2010",

doi = "10.1109/AUSCTW.2010.5426775",

language = "English",

isbn = "9781424454334",

series = "2010 Australian Communications Theory Workshop, AusCTW 2010",

pages = "97--101",

booktitle = "2010 Australian Communications Theory Workshop, AusCTW 2010",

note = "2010 Australian Communications Theory Workshop, AusCTW 2010 ; Conference date: 03-02-2010 Through 05-02-2010",

}

Wei, L, Kennedy, RA & Lamahewa, TA 2010, Signal concentration on unit sphere: A local K-th moment zenithal energy concentration measure. in 2010 Australian Communications Theory Workshop, AusCTW 2010., 5426775, 2010 Australian Communications Theory Workshop, AusCTW 2010, pp. 97-101, 2010 Australian Communications Theory Workshop, AusCTW 2010, Canberra, ACT, Australia, 3/02/10. https://doi.org/10.1109/AUSCTW.2010.5426775

Signal concentration on unit sphere: A local K-th moment zenithal energy concentration measure. / Wei, Liying; Kennedy, Rodney A.; Lamahewa, Tharaka A.
2010 Australian Communications Theory Workshop, AusCTW 2010. 2010. p. 97-101 5426775 (2010 Australian Communications Theory Workshop, AusCTW 2010).

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

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T2 - 2010 Australian Communications Theory Workshop, AusCTW 2010

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AU - Kennedy, Rodney A.

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N2 - We define a k-th moment zenithal energy concentration measure for a polar cap region on the unit sphere. The optimal functions are obtained with the maximal local k-th moment zenithal measure (LMZM). Compared to the spherical Slepian function in the cap region and the optimal function with the minimal global k-th moment zenithal measure (GMZM), we show that: 1) as k increases, the tail of the function with LMZM decays more quickly; 2) the main lobe of the optimal function with LMZM moves as the maximum colatitude of the cap increases; while the spherical Slepian function does not change much and the function with GMZM is by definition invariant; and 3) LMZM has no obvious advantage over the spherical Slepian function and the GMZM optimal function in both the energy concentration and tail decay rate.

AB - We define a k-th moment zenithal energy concentration measure for a polar cap region on the unit sphere. The optimal functions are obtained with the maximal local k-th moment zenithal measure (LMZM). Compared to the spherical Slepian function in the cap region and the optimal function with the minimal global k-th moment zenithal measure (GMZM), we show that: 1) as k increases, the tail of the function with LMZM decays more quickly; 2) the main lobe of the optimal function with LMZM moves as the maximum colatitude of the cap increases; while the spherical Slepian function does not change much and the function with GMZM is by definition invariant; and 3) LMZM has no obvious advantage over the spherical Slepian function and the GMZM optimal function in both the energy concentration and tail decay rate.

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M3 - Conference contribution

SN - 9781424454334

T3 - 2010 Australian Communications Theory Workshop, AusCTW 2010

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BT - 2010 Australian Communications Theory Workshop, AusCTW 2010

Y2 - 3 February 2010 through 5 February 2010

ER -

Signal concentration on unit sphere: A local K-th moment zenithal energy concentration measure

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