An optimal basis of band-limited functions for signal analysis and design

Liying Wei; Rodney A. Kennedy; Tharaka A. Lamahewa

doi:10.1109/TSP.2010.2057427

An optimal basis of band-limited functions for signal analysis and design

Liying Wei^*, Rodney A. Kennedy, Tharaka A. Lamahewa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

This paper studies signal concentration in the time and frequency domains using the general constrained variational method of Franks. The minimum k th (k=0,2,4....) moment time-duration measure for band-limited signals is formulated. A complete, orthonormal set of band-limited functions in L ²([-W,W]) with the minimum fourth-moment time-duration measure is obtained. Numerical investigations of our optimal 4th moment functions show: 1) less energy concentration in the main lobe than the prolate spheroidal wave functions (PSWF); 2) higher energy concentration in the main lobe than Gabor's function; and 3) a larger main lobe than both PSWF and Gabor. Applications for our basis functions include: 1) radar systems and high resolution communication systems, and 2) representation and approximation to any band-limited signal in a given time interval.

Original language	English
Article number	5508321
Pages (from-to)	5744-5755
Number of pages	12
Journal	IEEE Transactions on Signal Processing
Volume	58
Issue number	11
DOIs	https://doi.org/10.1109/TSP.2010.2057427
Publication status	Published - Nov 2010

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title = "An optimal basis of band-limited functions for signal analysis and design",

abstract = "This paper studies signal concentration in the time and frequency domains using the general constrained variational method of Franks. The minimum k th (k=0,2,4....) moment time-duration measure for band-limited signals is formulated. A complete, orthonormal set of band-limited functions in L 2([-W,W]) with the minimum fourth-moment time-duration measure is obtained. Numerical investigations of our optimal 4th moment functions show: 1) less energy concentration in the main lobe than the prolate spheroidal wave functions (PSWF); 2) higher energy concentration in the main lobe than Gabor's function; and 3) a larger main lobe than both PSWF and Gabor. Applications for our basis functions include: 1) radar systems and high resolution communication systems, and 2) representation and approximation to any band-limited signal in a given time interval.",

keywords = "Fraction out-of-band energy (FOBE), Gabor's function, orthonormal basis, prolate spheroidal wave function (PSWF), time-frequency",

author = "Liying Wei and Kennedy, \{Rodney A.\} and Lamahewa, \{Tharaka A.\}",

year = "2010",

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doi = "10.1109/TSP.2010.2057427",

language = "English",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - An optimal basis of band-limited functions for signal analysis and design

AU - Wei, Liying

AU - Kennedy, Rodney A.

AU - Lamahewa, Tharaka A.

PY - 2010/11

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N2 - This paper studies signal concentration in the time and frequency domains using the general constrained variational method of Franks. The minimum k th (k=0,2,4....) moment time-duration measure for band-limited signals is formulated. A complete, orthonormal set of band-limited functions in L 2([-W,W]) with the minimum fourth-moment time-duration measure is obtained. Numerical investigations of our optimal 4th moment functions show: 1) less energy concentration in the main lobe than the prolate spheroidal wave functions (PSWF); 2) higher energy concentration in the main lobe than Gabor's function; and 3) a larger main lobe than both PSWF and Gabor. Applications for our basis functions include: 1) radar systems and high resolution communication systems, and 2) representation and approximation to any band-limited signal in a given time interval.

AB - This paper studies signal concentration in the time and frequency domains using the general constrained variational method of Franks. The minimum k th (k=0,2,4....) moment time-duration measure for band-limited signals is formulated. A complete, orthonormal set of band-limited functions in L 2([-W,W]) with the minimum fourth-moment time-duration measure is obtained. Numerical investigations of our optimal 4th moment functions show: 1) less energy concentration in the main lobe than the prolate spheroidal wave functions (PSWF); 2) higher energy concentration in the main lobe than Gabor's function; and 3) a larger main lobe than both PSWF and Gabor. Applications for our basis functions include: 1) radar systems and high resolution communication systems, and 2) representation and approximation to any band-limited signal in a given time interval.

KW - Fraction out-of-band energy (FOBE)

KW - Gabor's function

KW - orthonormal basis

KW - prolate spheroidal wave function (PSWF)

KW - time-frequency

UR - https://www.scopus.com/pages/publications/79953818944

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DO - 10.1109/TSP.2010.2057427

M3 - Article

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VL - 58

SP - 5744

EP - 5755

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 11

M1 - 5508321

ER -

An optimal basis of band-limited functions for signal analysis and design

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