A Generalized Sampling Theorem for Frequency Localized Signals

A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is two-fold: (1) It applies to various prefilters effecting a “soft” bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obt...

Full description

Saved in:
Bibliographic Details
Published inSampling theory in signal and image processing Vol. 8; no. 2; pp. 127 - 146
Main Author Hammerich, Edwin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2009
Sampling Publishing
Subjects
Abstract Harmonic Analysis
Chebyshev approximation
Estimation theory
Hilbert space
Image and Speech Processing
Interpolation
Machine Learning
Mathematics
Methods
Properties
Sampling (Acoustical engineering)
Signal
Signal processing
error estimate
generalized Chebyshev inequality
interpolating function
critical sampling interval
Frequency localization
reproducing kernel Hilbert space
generalized sampling theorem
41A15
94A20
Online AccessGet full text
ISSN1530-6429
DOI10.1007/BF03549512

Cover

Abstract A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is two-fold: (1) It applies to various prefilters effecting a “soft” bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obtained (though the former might be “practically perfect” in many cases). For an arbitrary finite-energy signal the frequency localization is performed by a prefilter realizing a crosscorrelation with a function of prescribed properties. The range of the prefilter, the so-called localization space, is described in some detail. Regular sampling is applied and a reconstruction formula is given. For the reconstruction error a general error estimate is derived and connections between a critical sampling interval and notions of “soft bandwidth” for the prefilter are indicated. Examples based on the sinc-function, Gaussian functions, and B-splines are discussed.
AbstractList A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is two-fold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obtained (though the former might be "practically perfect" in many cases). For an arbitrary finite-energy signal the frequency localization is performed by a prefilter realizing a crosscorrelation with a function of prescribed properties. The range of the prefilter, the so-called localization space, is described in some detail. Regular sampling is applied and a reconstruction formula is given. For the reconstruction error a general error estimate is derived and connections between a critical sampling interval and notions of "soft bandwidth" for the prefilter are indicated. Examples based on the sine-function, Gaussian functions, and B-splines are discussed. Key words and phrases : Frequency localization, reproducing kernel Hilbert space, interpolating function, error estimate, generalized Chebyshev inequality, critical sampling interval, generalized sampling theorem. 2000 AMS Mathematics Subject Classification--94A20,41A15
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is two-fold: (1) It applies to various prefilters effecting a “soft” bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obtained (though the former might be “practically perfect” in many cases). For an arbitrary finite-energy signal the frequency localization is performed by a prefilter realizing a crosscorrelation with a function of prescribed properties. The range of the prefilter, the so-called localization space, is described in some detail. Regular sampling is applied and a reconstruction formula is given. For the reconstruction error a general error estimate is derived and connections between a critical sampling interval and notions of “soft bandwidth” for the prefilter are indicated. Examples based on the sinc-function, Gaussian functions, and B-splines are discussed.
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is two-fold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obtained (though the former might be "practically perfect" in many cases). For an arbitrary finite-energy signal the frequency localization is performed by a prefilter realizing a crosscorrelation with a function of prescribed properties. The range of the prefilter, the so-called localization space, is described in some detail. Regular sampling is applied and a reconstruction formula is given. For the reconstruction error a general error estimate is derived and connections between a critical sampling interval and notions of "soft bandwidth" for the prefilter are indicated. Examples based on the sine-function, Gaussian functions, and B-splines are discussed.
Audience Academic
Author Hammerich, Edwin
Author_xml – sequence: 1
  givenname: Edwin
  surname: Hammerich
  fullname: Hammerich, Edwin
  email: edwin.hammerich@ieee.org
  organization: Ministry of Defence
BookMark eNptkE9Lw0AQxfdQwbZ68RMEvCmp-7dpLkIttgoFD9Zz2Exm45Zkt27aQ_30bqkiSpnDg5nfmxnegPScd0jIFaMjRml29zCnQslcMd4jfaYETceS5-dk0HVrSuNE0D65nyYLdBh0Yz-xSl51u2msq5PVO_qAbWJ8SOYBP3boYJ8sPfyAtna66S7ImYmCl986JG_zx9XsKV2-LJ5n02UKXOY8BQGSG2ClpFiBxEyB1jiWOn6kM9DC5CArngFDpUw5kXkOpdSTcsJzqNCIIbk-7q11g4V1xm-DhtZ2UEw5HSvBpBSRGp2gYlXYWojpGBv7fww3RwME33UBTbEJttVhXzBaHEIsfkOMMP0Hg93qrfUuXrHNacvt0dLFva7GUKz9LhyCO0V_ASavg_U
CitedBy_id crossref_primary_10_1016_j_acha_2017_07_003
crossref_primary_10_1016_j_acha_2010_09_007
crossref_primary_10_1007_BF03549522
Cites_doi 10.1002/sapm195938168
10.1142/S0219691305000981
10.1109/JRPROC.1949.232969
10.1007/s00041-003-0004-2
10.1007/978-0-8176-8224-8
10.1109/78.330352
10.1090/qam/15914
10.1016/0165-1684(92)90030-Z
10.1007/BF03549426
10.1109/18.57199
10.1109/79.799930
10.1080/01630569408816545
10.1109/5.843002
10.1109/18.119745
10.1109/PROC.1977.10771
10.1137/1034002
10.1007/978-1-4612-0133-5
10.1007/BF03549405
10.1109/81.948437
10.1007/978-3-662-09922-3
10.1007/BF02570568
10.1007/BF03549464
10.1007/978-1-4613-9757-1_7
10.1109/TSP.2006.873488
10.1006/acha.1998.0249
10.1007/978-1-4612-0003-1
ContentType Journal Article
Copyright Sampling Publishing 2009
COPYRIGHT 2009 Sampling Publishing
Copyright_xml – notice: Sampling Publishing 2009
– notice: COPYRIGHT 2009 Sampling Publishing
DBID AAYXX
CITATION
DOI 10.1007/BF03549512
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList


DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Mathematics
EndPage 146
ExternalDocumentID A206531443
10_1007_BF03549512
GroupedDBID 123
1XV
29P
ABDBF
ALMA_UNASSIGNED_HOLDINGS
EBS
EJD
ESX
I-F
IAO
ICD
ISR
ITC
J9A
ROL
SJN
AAYXX
CITATION
ID FETCH-LOGICAL-c2492-c3c42fc1b40edc4e75caae64a642a7ca3f9c4d27c1e55fb8499cb4a8b829cdef3
ISSN 1530-6429
IngestDate Wed Mar 19 03:30:30 EDT 2025
Sat Mar 08 20:20:55 EST 2025
Thu Apr 24 22:50:35 EDT 2025
Tue Jul 01 01:33:13 EDT 2025
Fri Feb 21 02:47:54 EST 2025
IsPeerReviewed false
IsScholarly false
Issue 2
Keywords error estimate
generalized Chebyshev inequality
interpolating function
critical sampling interval
Frequency localization
reproducing kernel Hilbert space
generalized sampling theorem
41A15
94A20
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c2492-c3c42fc1b40edc4e75caae64a642a7ca3f9c4d27c1e55fb8499cb4a8b829cdef3
PageCount 20
ParticipantIDs gale_infotracmisc_A206531443
gale_infotracacademiconefile_A206531443
crossref_primary_10_1007_BF03549512
crossref_citationtrail_10_1007_BF03549512
springer_journals_10_1007_BF03549512
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 20090500
2009-05-00
20090501
PublicationDateYYYYMMDD 2009-05-01
PublicationDate_xml – month: 5
  year: 2009
  text: 20090500
PublicationDecade 2000
PublicationPlace Cham
PublicationPlace_xml – name: Cham
PublicationTitle Sampling theory in signal and image processing
PublicationTitleAbbrev STSIP
PublicationYear 2009
Publisher Springer International Publishing
Sampling Publishing
Publisher_xml – name: Springer International Publishing
– name: Sampling Publishing
References Butzer, Stens (CR6) 1992; 34
Hammerich (CR16) 2004; 3
Schoenberg (CR23) 1946; 4
Aldroubi, Unser (CR2) 1994; 15
Jerri, Marks (CR19) 1993
Walter (CR30) 1992; 38
Daubechies (CR8) 1990; 36
Hammerich (CR17) 2007; 6
CR13
Young (CR31) 2001
Feichtinger, Strohmer ed (CR12) 2003
Eldar, Dvorkind (CR11) 2006; 54
Maz'ja (CR21) 1985
Unser (CR27) 1999; 16
Blu, Unser (CR3) 1999; 6
Christensen (CR7) 2003
Vaidyanathan (CR29) 2001; 48
Eldar (CR9) 2003; 9
Gabor (CR14) 1946; 93
Aldroubi, Unser, Eden (CR1) 1992; 28
Jerri (CR18) 1977; 65
Shannon (CR24) 1949; 37
Unser, Aldroubi (CR26) 1994; 42
Unser (CR28) 2000; 88
Butzer, Splettstösser, Stens (CR5) 1988; 90
Sun (CR25) 2005; 4
Eldar, Werther (CR10) 2005; 3
Kramer (CR20) 1959; 38
Nashed, Walter (CR22) 1991; 4
Gröchenig (CR15) 2001
de Boor, DeVore, Ron (CR4) 1994; 341
HG Feichtinger (BF03549512_CR12) 2003
YC Eldar (BF03549512_CR10) 2005; 3
W Sun (BF03549512_CR25) 2005; 4
AJ Jerri (BF03549512_CR19) 1993
C de Boor (BF03549512_CR4) 1994; 341
A Aldroubi (BF03549512_CR1) 1992; 28
K Gröchenig (BF03549512_CR15) 2001
AJ Jerri (BF03549512_CR18) 1977; 65
O Christensen (BF03549512_CR7) 2003
PP Vaidyanathan (BF03549512_CR29) 2001; 48
M Unser (BF03549512_CR27) 1999; 16
YC Eldar (BF03549512_CR9) 2003; 9
PL Butzer (BF03549512_CR5) 1988; 90
VG Maz'ja (BF03549512_CR21) 1985
MZ Nashed (BF03549512_CR22) 1991; 4
IJ Schoenberg (BF03549512_CR23) 1946; 4
YC Eldar (BF03549512_CR11) 2006; 54
RM Young (BF03549512_CR31) 2001
BF03549512_CR13
I Daubechies (BF03549512_CR8) 1990; 36
T Blu (BF03549512_CR3) 1999; 6
A Aldroubi (BF03549512_CR2) 1994; 15
E Hammerich (BF03549512_CR17) 2007; 6
CE Shannon (BF03549512_CR24) 1949; 37
M Unser (BF03549512_CR26) 1994; 42
HP Kramer (BF03549512_CR20) 1959; 38
M Unser (BF03549512_CR28) 2000; 88
E Hammerich (BF03549512_CR16) 2004; 3
D Gabor (BF03549512_CR14) 1946; 93
GG Walter (BF03549512_CR30) 1992; 38
PL Butzer (BF03549512_CR6) 1992; 34
References_xml – volume: 38
  start-page: 68
  year: 1959
  end-page: 72
  ident: CR20
  article-title: A generalized sampling theorem
  publication-title: J. Math. and Phys.
  doi: 10.1002/sapm195938168
– volume: 3
  start-page: 497
  year: 2005
  end-page: 509
  ident: CR10
  article-title: General framework for consistent sampling in Hilbert spaces
  publication-title: Int. J. of Wavelets, Multiresolution and Inform. Process.
  doi: 10.1142/S0219691305000981
– volume: 37
  start-page: 10
  year: 1949
  end-page: 21
  ident: CR24
  article-title: Communication in the presence of noise
  publication-title: Proc. IRE
  doi: 10.1109/JRPROC.1949.232969
– volume: 9
  start-page: 77
  year: 2003
  end-page: 96
  ident: CR9
  article-title: Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors
  publication-title: J. Fourier Anal. Appl.
  doi: 10.1007/s00041-003-0004-2
– year: 2003
  ident: CR7
  publication-title: An Introduction to Frames and Riesz Bases
  doi: 10.1007/978-0-8176-8224-8
– volume: 42
  start-page: 2915
  year: 1994
  end-page: 2925
  ident: CR26
  article-title: A general sampling theory for nonideal acquisition devices
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/78.330352
– volume: 4
  start-page: 45
  year: 1946
  end-page: 99, 112-141
  ident: CR23
  article-title: Contribution to the problem of approximation of equidistant data by analytic functions
  publication-title: Quart. Appl. Math.
  doi: 10.1090/qam/15914
– volume: 28
  start-page: 127
  year: 1992
  end-page: 138
  ident: CR1
  article-title: Cardinal spline filters: Stability and convergence to the ideal sinc interpolator
  publication-title: Signal Process.
  doi: 10.1016/0165-1684(92)90030-Z
– volume: 4
  start-page: 73
  year: 2005
  end-page: 98
  ident: CR25
  article-title: Sampling theorems for multivariate shift invariant subspaces
  publication-title: Sampl. Theory Signal Image Process.
  doi: 10.1007/BF03549426
– volume: 90
  start-page: 1
  year: 1988
  end-page: 70
  ident: CR5
  article-title: The sampling theorem and linear prediction in signal analysis
  publication-title: Jber. d. Dt. Math.-Verein.
– volume: 36
  start-page: 961
  year: 1990
  end-page: 1005
  ident: CR8
  article-title: The wavelet transform, time-frequency localization and signal analysis
  publication-title: IEEE Trans. Inform. Theory
  doi: 10.1109/18.57199
– volume: 16
  start-page: 22
  year: 1999
  end-page: 38
  ident: CR27
  article-title: Splines: A perfect fit for signal and image processing
  publication-title: IEEE Signal Process. Mag.
  doi: 10.1109/79.799930
– volume: 15
  start-page: 1
  year: 1994
  end-page: 21
  ident: CR2
  article-title: Sampling procedures in function spaces and asymptotic equivalence with Shannon's sampling theory
  publication-title: Numer. Fund. Anal. and Optimiz.
  doi: 10.1080/01630569408816545
– volume: 88
  start-page: 569
  year: 2000
  end-page: 587
  ident: CR28
  article-title: Sampling - 50 years after Shannon
  publication-title: Proc. IEEE
  doi: 10.1109/5.843002
– volume: 38
  start-page: 881
  year: 1992
  end-page: 884
  ident: CR30
  article-title: A sampling theorem for wavelet subspaces
  publication-title: IEEE Trans. Inform. Theory
  doi: 10.1109/18.119745
– volume: 65
  start-page: 1565
  year: 1977
  end-page: 1596
  ident: CR18
  article-title: The Shannon sampling theorem - Its various extensions and applications: A tutorial review
  publication-title: Proc. IEEE
  doi: 10.1109/PROC.1977.10771
– volume: 34
  start-page: 40
  year: 1992
  end-page: 53
  ident: CR6
  article-title: Sampling theory for not necessarily band-limited functions: A historical overview
  publication-title: SIAM Review
  doi: 10.1137/1034002
– year: 2003
  ident: CR12
  publication-title: Advances in Gabor Analysis
  doi: 10.1007/978-1-4612-0133-5
– volume: 3
  start-page: 45
  year: 2004
  end-page: 81
  ident: CR16
  article-title: A sampling theorem for time-frequency localized signals
  publication-title: Sampl. Theory Signal Image Process.
  doi: 10.1007/BF03549405
– volume: 48
  start-page: 1094
  year: 2001
  end-page: 1109
  ident: CR29
  article-title: Generalizations of the sampling theorem: Seven decades after Nyquist
  publication-title: IEEE Trans. Circuit Syst. I
  doi: 10.1109/81.948437
– year: 1985
  ident: CR21
  publication-title: Sobolev Spaces
  doi: 10.1007/978-3-662-09922-3
– ident: CR13
– volume: 4
  start-page: 363
  year: 1991
  end-page: 390
  ident: CR22
  article-title: General sampling theorems for functions in reproducing kernel Hilbert spaces
  publication-title: Math. Control, Signals, Syst.
  doi: 10.1007/BF02570568
– volume: 6
  start-page: 71
  year: 2007
  end-page: 86
  ident: CR17
  article-title: Sampling in shift-invariant spaces with Gaussian generator
  publication-title: Sampl. Theory Signal Image Process.
  doi: 10.1007/BF03549464
– start-page: 219
  year: 1993
  end-page: 298
  ident: CR19
  article-title: Error analysis in application of generalizations of the sampling theorem
  publication-title: Advanced topics in Shannon sampling and interpolation theory
  doi: 10.1007/978-1-4613-9757-1_7
– year: 2001
  ident: CR31
  publication-title: An Introduction to Nonharmonic Fourier Series (Revised First Edition)
– volume: 54
  start-page: 2155
  year: 2006
  end-page: 2167
  ident: CR11
  article-title: A minimum squared-error framework for generalized sampling
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2006.873488
– volume: 341
  start-page: 787
  year: 1994
  end-page: 806
  ident: CR4
  article-title: Approximation from shift-invariant subspaces of (ℝ )
  publication-title: Trans. Amer. Math. Soc.
– volume: 93
  start-page: 429
  year: 1946
  end-page: 457
  ident: CR14
  article-title: Theory of communication
  publication-title: J. Inst. Elect. Eng.
– volume: 6
  start-page: 219
  year: 1999
  end-page: 251
  ident: CR3
  article-title: Approximation error for quasi-interpolators and (multi-)wavelet expansions
  publication-title: Appl. Comput. Harmon. Anal.
  doi: 10.1006/acha.1998.0249
– year: 2001
  ident: CR15
  publication-title: Foundations of Time-Frequency Analysis
  doi: 10.1007/978-1-4612-0003-1
– volume: 54
  start-page: 2155
  year: 2006
  ident: BF03549512_CR11
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2006.873488
– ident: BF03549512_CR13
– volume: 42
  start-page: 2915
  year: 1994
  ident: BF03549512_CR26
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/78.330352
– volume: 6
  start-page: 71
  year: 2007
  ident: BF03549512_CR17
  publication-title: Sampl. Theory Signal Image Process.
  doi: 10.1007/BF03549464
– volume: 4
  start-page: 363
  year: 1991
  ident: BF03549512_CR22
  publication-title: Math. Control, Signals, Syst.
  doi: 10.1007/BF02570568
– volume: 38
  start-page: 68
  year: 1959
  ident: BF03549512_CR20
  publication-title: J. Math. and Phys.
  doi: 10.1002/sapm195938168
– volume-title: Foundations of Time-Frequency Analysis
  year: 2001
  ident: BF03549512_CR15
  doi: 10.1007/978-1-4612-0003-1
– volume: 3
  start-page: 45
  year: 2004
  ident: BF03549512_CR16
  publication-title: Sampl. Theory Signal Image Process.
  doi: 10.1007/BF03549405
– volume: 65
  start-page: 1565
  year: 1977
  ident: BF03549512_CR18
  publication-title: Proc. IEEE
  doi: 10.1109/PROC.1977.10771
– volume-title: Sobolev Spaces
  year: 1985
  ident: BF03549512_CR21
  doi: 10.1007/978-3-662-09922-3
– volume: 37
  start-page: 10
  year: 1949
  ident: BF03549512_CR24
  publication-title: Proc. IRE
  doi: 10.1109/JRPROC.1949.232969
– volume: 38
  start-page: 881
  year: 1992
  ident: BF03549512_CR30
  publication-title: IEEE Trans. Inform. Theory
  doi: 10.1109/18.119745
– volume: 28
  start-page: 127
  year: 1992
  ident: BF03549512_CR1
  publication-title: Signal Process.
  doi: 10.1016/0165-1684(92)90030-Z
– volume: 4
  start-page: 73
  year: 2005
  ident: BF03549512_CR25
  publication-title: Sampl. Theory Signal Image Process.
  doi: 10.1007/BF03549426
– volume: 48
  start-page: 1094
  year: 2001
  ident: BF03549512_CR29
  publication-title: IEEE Trans. Circuit Syst. I
  doi: 10.1109/81.948437
– volume: 6
  start-page: 219
  year: 1999
  ident: BF03549512_CR3
  publication-title: Appl. Comput. Harmon. Anal.
  doi: 10.1006/acha.1998.0249
– volume: 88
  start-page: 569
  year: 2000
  ident: BF03549512_CR28
  publication-title: Proc. IEEE
  doi: 10.1109/5.843002
– volume-title: An Introduction to Frames and Riesz Bases
  year: 2003
  ident: BF03549512_CR7
  doi: 10.1007/978-0-8176-8224-8
– volume: 93
  start-page: 429
  year: 1946
  ident: BF03549512_CR14
  publication-title: J. Inst. Elect. Eng.
– volume: 3
  start-page: 497
  year: 2005
  ident: BF03549512_CR10
  publication-title: Int. J. of Wavelets, Multiresolution and Inform. Process.
  doi: 10.1142/S0219691305000981
– volume: 15
  start-page: 1
  year: 1994
  ident: BF03549512_CR2
  publication-title: Numer. Fund. Anal. and Optimiz.
  doi: 10.1080/01630569408816545
– volume-title: Advances in Gabor Analysis
  year: 2003
  ident: BF03549512_CR12
  doi: 10.1007/978-1-4612-0133-5
– volume: 36
  start-page: 961
  year: 1990
  ident: BF03549512_CR8
  publication-title: IEEE Trans. Inform. Theory
  doi: 10.1109/18.57199
– volume: 4
  start-page: 45
  year: 1946
  ident: BF03549512_CR23
  publication-title: Quart. Appl. Math.
  doi: 10.1090/qam/15914
– volume: 90
  start-page: 1
  year: 1988
  ident: BF03549512_CR5
  publication-title: Jber. d. Dt. Math.-Verein.
– volume-title: An Introduction to Nonharmonic Fourier Series (Revised First Edition)
  year: 2001
  ident: BF03549512_CR31
– volume: 16
  start-page: 22
  year: 1999
  ident: BF03549512_CR27
  publication-title: IEEE Signal Process. Mag.
  doi: 10.1109/79.799930
– volume: 341
  start-page: 787
  year: 1994
  ident: BF03549512_CR4
  publication-title: Trans. Amer. Math. Soc.
– start-page: 219
  volume-title: Advanced topics in Shannon sampling and interpolation theory
  year: 1993
  ident: BF03549512_CR19
  doi: 10.1007/978-1-4613-9757-1_7
– volume: 9
  start-page: 77
  year: 2003
  ident: BF03549512_CR9
  publication-title: J. Fourier Anal. Appl.
  doi: 10.1007/s00041-003-0004-2
– volume: 34
  start-page: 40
  year: 1992
  ident: BF03549512_CR6
  publication-title: SIAM Review
  doi: 10.1137/1034002
SSID ssj0054930
Score 1.4557685
Snippet A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is two-fold: (1) It applies...
SourceID gale
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 127
SubjectTerms Abstract Harmonic Analysis
Chebyshev approximation
Estimation theory
Hilbert space
Image and Speech Processing
Interpolation
Machine Learning
Mathematics
Methods
Properties
Sampling (Acoustical engineering)
Signal
Signal processing
Title A Generalized Sampling Theorem for Frequency Localized Signals
URI https://link.springer.com/article/10.1007/BF03549512
Volume 8
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFA5eXvRBvOK8EVAQkcqWprcXoV6GiPq0wd5KkqYy0CluIvrrPUmTtHV7UF_K1px0Xb4255JzviB0lEQStFII3kmUxx6VUnpchtxjHT8PRRK3C51Vef8Q3vTp7SAYVBsX6uqSCT8TXzPrSv6DKpwDXFWV7B-QdReFE_AZ8IUjIAzHX2GcWtbo4ZeyG5nKDgfPX9fby2edQdh9K3OlP0_vlNYqBYePijW5bpe6vrqwUdcCjrVUubjwrDJ7XsuaAqvrXNh7WO4mdZ1_GBZvG0RIqpS9RhDxRxiyioQ1ZkjwN6kJU5gpNK49KaQ2HXbKun-jWU2wcWrSbrtUdHBWA5NV3STBtuTKldA8WiRRpFbmF9OLq4uuVb_QqjeYcffZ5KQ1vRtWiNXFzZVwbWD0VtGK8QxwWsK8hubkaB0t1_gi4du9I9kdb6DzFNfgxxZCbODHAD928GMHPzbwb6J-97p3eeOZ7TA8oWgdPeELSgrR4bQtc0FlFAjGZEgZ_EsWCeYXiaA5iURHBkHBY_BlBacs5jFJRC4LfwstjF5GchthsNqSnIREFoFPA054CF19CSNHEgZtLXRihycThitebVnylE0D0UKHTva1ZEiZKXWsRjlTwMOVBDPVH3A_ioAsS4kiSQbv3m-hvYYkTHei0XxkccrMqzie8Xs7vxPbRUvV67CHFiZv73IfrMwJPzDP1Tdtsnt-
linkProvider EBSCOhost
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Generalized+Sampling+Theorem+for+Frequency+Localized+Signals&rft.jtitle=Sampling+theory+in+signal+and+image+processing&rft.au=Hammerich%2C+Edwin&rft.date=2009-05-01&rft.pub=Springer+International+Publishing&rft.issn=1530-6429&rft.volume=8&rft.issue=2&rft.spage=127&rft.epage=146&rft_id=info:doi/10.1007%2FBF03549512&rft.externalDocID=10_1007_BF03549512
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1530-6429&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1530-6429&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1530-6429&client=summon