Generalized sampling expansion for functions on the sphere
Generalized sampling expansion for functions on the sphere
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.
5870-5879
Ben Hagai, Ilan
64797593-3fdb-4421-9519-c918d26c672d
Fazi, Filippo Maria
e5aefc08-ab45-47c1-ad69-c3f12d07d807
Rafaely, Boaz
0839a7e8-bdbc-4f46-b57b-a9e5c625e968
November 2012
Ben Hagai, Ilan
64797593-3fdb-4421-9519-c918d26c672d
Fazi, Filippo Maria
e5aefc08-ab45-47c1-ad69-c3f12d07d807
Rafaely, Boaz
0839a7e8-bdbc-4f46-b57b-a9e5c625e968
Ben Hagai, Ilan, Fazi, Filippo Maria and Rafaely, Boaz
(2012)
Generalized sampling expansion for functions on the sphere.
IEEE Transactions on Signal Processing, 60 (11), .
(doi:10.1109/TSP.2012.2210549).
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.
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e-pub ahead of print date: 27 July 2012
Published date: November 2012
Organisations:
Acoustics Group
Identifiers
Local EPrints ID: 343518
URI: http://eprints.soton.ac.uk/id/eprint/343518
ISSN: 1053-587X
PURE UUID: 64a77f4a-e121-4037-a6b3-af0fe7bb3505
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Date deposited: 08 Oct 2012 14:21
Last modified: 15 Mar 2024 03:32
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Author:
Ilan Ben Hagai
Author:
Boaz Rafaely
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