Reproducing kernel structure and sampling on time-warped Kramer spaces

Shahrnaz Azizi, Douglas Cochran

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

Given a signal space of functions on the real line, a time-warped signal space consists of all signals that can be formed by composition of signals in the original space with an invertible real-valued function. Clark's theorem shows that signals formed by warping bandlimited signals admit formulae for reconstruction from samples. This paper considers time warping of more general signal spaces in which Kramer's generalized sampling theorem applies and observes that such spaces admit sampling and reconstruction formulae. This observation motivates the question of whether Kramer's theorem applies directly to the warped space, which is answered affirmatively by introduction of a suitable reproducing kernel Hilbert space structure. This result generalizes one of Zeevi, who pointed out that Clark's theorem is a consequence of Kramer's.

Original languageEnglish (US)
Title of host publicationICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
PublisherIEEE
Pages1649-1652
Number of pages4
Volume3
StatePublished - 1999
EventProceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99) - Phoenix, AZ, USA
Duration: Mar 15 1999Mar 19 1999

Other

OtherProceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99)
CityPhoenix, AZ, USA
Period3/15/993/19/99

Fingerprint

sampling
Sampling
Hilbert spaces
theorems
Chemical analysis
time signals
Hilbert space

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Acoustics and Ultrasonics

Cite this

Azizi, S., & Cochran, D. (1999). Reproducing kernel structure and sampling on time-warped Kramer spaces. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings (Vol. 3, pp. 1649-1652). IEEE.

Reproducing kernel structure and sampling on time-warped Kramer spaces. / Azizi, Shahrnaz; Cochran, Douglas.

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. Vol. 3 IEEE, 1999. p. 1649-1652.

Research output: Chapter in Book/Report/Conference proceedingChapter

Azizi, S & Cochran, D 1999, Reproducing kernel structure and sampling on time-warped Kramer spaces. in ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. vol. 3, IEEE, pp. 1649-1652, Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99), Phoenix, AZ, USA, 3/15/99.
Azizi S, Cochran D. Reproducing kernel structure and sampling on time-warped Kramer spaces. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. Vol. 3. IEEE. 1999. p. 1649-1652
Azizi, Shahrnaz ; Cochran, Douglas. / Reproducing kernel structure and sampling on time-warped Kramer spaces. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. Vol. 3 IEEE, 1999. pp. 1649-1652
@inbook{9e2403b3ce034b2e944105ad649a0c1a,
title = "Reproducing kernel structure and sampling on time-warped Kramer spaces",
abstract = "Given a signal space of functions on the real line, a time-warped signal space consists of all signals that can be formed by composition of signals in the original space with an invertible real-valued function. Clark's theorem shows that signals formed by warping bandlimited signals admit formulae for reconstruction from samples. This paper considers time warping of more general signal spaces in which Kramer's generalized sampling theorem applies and observes that such spaces admit sampling and reconstruction formulae. This observation motivates the question of whether Kramer's theorem applies directly to the warped space, which is answered affirmatively by introduction of a suitable reproducing kernel Hilbert space structure. This result generalizes one of Zeevi, who pointed out that Clark's theorem is a consequence of Kramer's.",
author = "Shahrnaz Azizi and Douglas Cochran",
year = "1999",
language = "English (US)",
volume = "3",
pages = "1649--1652",
booktitle = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "IEEE",

}

TY - CHAP

T1 - Reproducing kernel structure and sampling on time-warped Kramer spaces

AU - Azizi, Shahrnaz

AU - Cochran, Douglas

PY - 1999

Y1 - 1999

N2 - Given a signal space of functions on the real line, a time-warped signal space consists of all signals that can be formed by composition of signals in the original space with an invertible real-valued function. Clark's theorem shows that signals formed by warping bandlimited signals admit formulae for reconstruction from samples. This paper considers time warping of more general signal spaces in which Kramer's generalized sampling theorem applies and observes that such spaces admit sampling and reconstruction formulae. This observation motivates the question of whether Kramer's theorem applies directly to the warped space, which is answered affirmatively by introduction of a suitable reproducing kernel Hilbert space structure. This result generalizes one of Zeevi, who pointed out that Clark's theorem is a consequence of Kramer's.

AB - Given a signal space of functions on the real line, a time-warped signal space consists of all signals that can be formed by composition of signals in the original space with an invertible real-valued function. Clark's theorem shows that signals formed by warping bandlimited signals admit formulae for reconstruction from samples. This paper considers time warping of more general signal spaces in which Kramer's generalized sampling theorem applies and observes that such spaces admit sampling and reconstruction formulae. This observation motivates the question of whether Kramer's theorem applies directly to the warped space, which is answered affirmatively by introduction of a suitable reproducing kernel Hilbert space structure. This result generalizes one of Zeevi, who pointed out that Clark's theorem is a consequence of Kramer's.

UR - http://www.scopus.com/inward/record.url?scp=0032627314&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032627314&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0032627314

VL - 3

SP - 1649

EP - 1652

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

PB - IEEE

ER -