Generalized sampling expansion for functions on the sphere

Ilan Ben Hagai; Filippo Maria Fazi; Boaz Rafaely

doi:10.1109/TSP.2012.2210549

Generalized sampling expansion for functions on the sphere

Ilan Ben Hagai, Filippo Maria Fazi, Boaz Rafaely

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Functions on the sphere appear in several applications, including geodesics, imaging and acoustics. Sampling of these functions may result in aliasing if the sampling condition is not met. The generalized sampling expansion introduced by Papoulis enables the reconstruction of a band-limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. This paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition, facilitating sub-Nyquit sampling without aliasing error. An analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented. Examples demonstrating the performance of the method and its limitations are studied.

Original language	English
Article number	6252066
Pages (from-to)	5870-5879
Number of pages	10
Journal	IEEE Transactions on Signal Processing
Volume	60
Issue number	11
DOIs	https://doi.org/10.1109/TSP.2012.2210549
State	Published - 22 Oct 2012

Keywords

Aliasing
generalized sampling expansion
spherical harmonics

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2012.2210549

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title = "Generalized sampling expansion for functions on the sphere",

abstract = "Functions on the sphere appear in several applications, including geodesics, imaging and acoustics. Sampling of these functions may result in aliasing if the sampling condition is not met. The generalized sampling expansion introduced by Papoulis enables the reconstruction of a band-limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. This paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition, facilitating sub-Nyquit sampling without aliasing error. An analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented. Examples demonstrating the performance of the method and its limitations are studied.",

keywords = "Aliasing, generalized sampling expansion, spherical harmonics",

author = "{Ben Hagai}, Ilan and Fazi, {Filippo Maria} and Boaz Rafaely",

note = "Funding Information: Manuscript received November 25, 2011; revised March 14, 2012 and June 25, 2012; accepted June 29, 2012. Date of publication July 27, 2012; date of current version nulldate. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Xiang‐Gen Xia. This research was partially supported by the Israel Science Foundation (ISF grant no. 155/06) and by the U.K. Royal Academy of Engineering and by the Engineering and Physical Sciences Research Council. This work has been partially funded by the Royal Academy of Engineering and by the Engineering and Physical Sciences Research Council.",

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AU - Ben Hagai, Ilan

AU - Fazi, Filippo Maria

AU - Rafaely, Boaz

N1 - Funding Information: Manuscript received November 25, 2011; revised March 14, 2012 and June 25, 2012; accepted June 29, 2012. Date of publication July 27, 2012; date of current version nulldate. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Xiang‐Gen Xia. This research was partially supported by the Israel Science Foundation (ISF grant no. 155/06) and by the U.K. Royal Academy of Engineering and by the Engineering and Physical Sciences Research Council. This work has been partially funded by the Royal Academy of Engineering and by the Engineering and Physical Sciences Research Council.

PY - 2012/10/22

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N2 - Functions on the sphere appear in several applications, including geodesics, imaging and acoustics. Sampling of these functions may result in aliasing if the sampling condition is not met. The generalized sampling expansion introduced by Papoulis enables the reconstruction of a band-limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. This paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition, facilitating sub-Nyquit sampling without aliasing error. An analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented. Examples demonstrating the performance of the method and its limitations are studied.

AB - Functions on the sphere appear in several applications, including geodesics, imaging and acoustics. Sampling of these functions may result in aliasing if the sampling condition is not met. The generalized sampling expansion introduced by Papoulis enables the reconstruction of a band-limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. This paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition, facilitating sub-Nyquit sampling without aliasing error. An analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented. Examples demonstrating the performance of the method and its limitations are studied.

KW - Aliasing

KW - generalized sampling expansion

KW - spherical harmonics

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JF - IEEE Transactions on Signal Processing

IS - 11

M1 - 6252066

ER -

Generalized sampling expansion for functions on the sphere

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Keywords

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