Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces

Xiang Gen Xia; Zhen Zhang

Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces

Xiang Gen Xia^*
, Zhen Zhang

^*Corresponding author for this work

University of Southern California

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

4 Citations (Scopus)

Abstract

The classical Shannon sampling theorem has been extended to wavelet subspaces by Walter, that is, a signal f(t) in certain wavelet subspace V_J(φ) for certain scaling function φ(t) can be exactly reconstructed by its samples f(k/2^J). For signals not necessarily in wavelet subspaces, the sampling theorem is not true. In this article, we estimate the aliasing error in the sampling theorem for a general signal. An application for the aliasing error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed.

Original language	English
Title of host publication	Digital Speech Processing
Publisher	Publ by IEEE
Pages	111.300-303
ISBN (Print)	0780309464
Publication status	Published - 1993
Externally published	Yes
Event	1993 IEEE International Conference on Acoustics, Speech and Signal Processing - Minneapolis, MN, USA Duration: 27 Apr 1993 → 30 Apr 1993

Publication series

Name	Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
Volume	3
ISSN (Print)	0736-7791

Conference

Conference	1993 IEEE International Conference on Acoustics, Speech and Signal Processing
City	Minneapolis, MN, USA
Period	27/04/93 → 30/04/93

Cite this

@inproceedings{faaf0601e49e4a62900ab7db9045db09,

title = "Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces",

abstract = "The classical Shannon sampling theorem has been extended to wavelet subspaces by Walter, that is, a signal f(t) in certain wavelet subspace VJ(φ) for certain scaling function φ(t) can be exactly reconstructed by its samples f(k/2J). For signals not necessarily in wavelet subspaces, the sampling theorem is not true. In this article, we estimate the aliasing error in the sampling theorem for a general signal. An application for the aliasing error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed.",

author = "Xia, \{Xiang Gen\} and Zhen Zhang",

year = "1993",

language = "English",

isbn = "0780309464",

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

publisher = "Publ by IEEE",

pages = "111.300--303",

booktitle = "Digital Speech Processing",

note = "1993 IEEE International Conference on Acoustics, Speech and Signal Processing ; Conference date: 27-04-1993 Through 30-04-1993",

}

Xia, XG & Zhang, Z 1993, Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces. in Digital Speech Processing. Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3, Publ by IEEE, pp. 111.300-303, 1993 IEEE International Conference on Acoustics, Speech and Signal Processing, Minneapolis, MN, USA, 27/04/93.

Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces. / Xia, Xiang Gen; Zhang, Zhen.
Digital Speech Processing. Publ by IEEE, 1993. p. 111.300-303 (Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing; Vol. 3).

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

TY - GEN

T1 - Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces

AU - Xia, Xiang Gen

AU - Zhang, Zhen

PY - 1993

Y1 - 1993

N2 - The classical Shannon sampling theorem has been extended to wavelet subspaces by Walter, that is, a signal f(t) in certain wavelet subspace VJ(φ) for certain scaling function φ(t) can be exactly reconstructed by its samples f(k/2J). For signals not necessarily in wavelet subspaces, the sampling theorem is not true. In this article, we estimate the aliasing error in the sampling theorem for a general signal. An application for the aliasing error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed.

AB - The classical Shannon sampling theorem has been extended to wavelet subspaces by Walter, that is, a signal f(t) in certain wavelet subspace VJ(φ) for certain scaling function φ(t) can be exactly reconstructed by its samples f(k/2J). For signals not necessarily in wavelet subspaces, the sampling theorem is not true. In this article, we estimate the aliasing error in the sampling theorem for a general signal. An application for the aliasing error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed.

UR - https://www.scopus.com/pages/publications/0027210166

M3 - Conference contribution

AN - SCOPUS:0027210166

SN - 0780309464

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

SP - 111.300-303

BT - Digital Speech Processing

PB - Publ by IEEE

T2 - 1993 IEEE International Conference on Acoustics, Speech and Signal Processing

Y2 - 27 April 1993 through 30 April 1993

ER -

Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces

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