TY - JOUR
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
Y1 - 2010/11
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 - http://www.scopus.com/inward/record.url?scp=79953818944&partnerID=8YFLogxK
U2 - 10.1109/TSP.2010.2057427
DO - 10.1109/TSP.2010.2057427
M3 - Article
SN - 1053-587X
VL - 58
SP - 5744
EP - 5755
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 11
M1 - 5508321
ER -