Theory of the Optimum Sub-Band Interpolation of Signals Using a Measure of Error in the Frequency Domain
Summary :
In this paper, we consider an extended form of the optimum sub-band interpolation for a family of band limited signals. It is assumed that this family of signals is a certain subset of the set of the signals whose Fourier spectrums have weighted L2 norms smaller than a given positive number. We use the sample values of the output signals of the finite number of linear systems excited, at the same time, by a band limited signal to be restored approximately. The proposed method minimizes the measure of error which is equal to the envelope of the approximation errors in the frequency domain. It is proved that the presented method is the optimum, in a certain sense, among all the linear and the nonlinear approximations using the same sample values of the signal.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E73-E No.10 pp.1611-1615
- Publication Date
- 1990/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Issue on Communication Theory and Its Applications)
- Category
- Signal Processing and Image Compression
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Takuro KIDA, "Theory of the Optimum Sub-Band Interpolation of Signals Using a Measure of Error in the Frequency Domain" in IEICE TRANSACTIONS on transactions,
vol. E73-E, no. 10, pp. 1611-1615, October 1990, doi: .
Abstract: In this paper, we consider an extended form of the optimum sub-band interpolation for a family of band limited signals. It is assumed that this family of signals is a certain subset of the set of the signals whose Fourier spectrums have weighted L2 norms smaller than a given positive number. We use the sample values of the output signals of the finite number of linear systems excited, at the same time, by a band limited signal to be restored approximately. The proposed method minimizes the measure of error which is equal to the envelope of the approximation errors in the frequency domain. It is proved that the presented method is the optimum, in a certain sense, among all the linear and the nonlinear approximations using the same sample values of the signal.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e73-e_10_1611/_p
Copy
@ARTICLE{e73-e_10_1611,
author={Takuro KIDA, },
journal={IEICE TRANSACTIONS on transactions},
title={Theory of the Optimum Sub-Band Interpolation of Signals Using a Measure of Error in the Frequency Domain},
year={1990},
volume={E73-E},
number={10},
pages={1611-1615},
abstract={In this paper, we consider an extended form of the optimum sub-band interpolation for a family of band limited signals. It is assumed that this family of signals is a certain subset of the set of the signals whose Fourier spectrums have weighted L2 norms smaller than a given positive number. We use the sample values of the output signals of the finite number of linear systems excited, at the same time, by a band limited signal to be restored approximately. The proposed method minimizes the measure of error which is equal to the envelope of the approximation errors in the frequency domain. It is proved that the presented method is the optimum, in a certain sense, among all the linear and the nonlinear approximations using the same sample values of the signal.},
keywords={},
doi={},
ISSN={},
month={October},}
Copy
TY - JOUR
TI - Theory of the Optimum Sub-Band Interpolation of Signals Using a Measure of Error in the Frequency Domain
T2 - IEICE TRANSACTIONS on transactions
SP - 1611
EP - 1615
AU - Takuro KIDA
PY - 1990
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E73-E
IS - 10
JA - IEICE TRANSACTIONS on transactions
Y1 - October 1990
AB - In this paper, we consider an extended form of the optimum sub-band interpolation for a family of band limited signals. It is assumed that this family of signals is a certain subset of the set of the signals whose Fourier spectrums have weighted L2 norms smaller than a given positive number. We use the sample values of the output signals of the finite number of linear systems excited, at the same time, by a band limited signal to be restored approximately. The proposed method minimizes the measure of error which is equal to the envelope of the approximation errors in the frequency domain. It is proved that the presented method is the optimum, in a certain sense, among all the linear and the nonlinear approximations using the same sample values of the signal.
ER -
English
