An Optimal Basis of Band-Limited Functions for Signal Analysis and Design

作者：Wei Liying^*; Kennedy Rodney A; Lamahewa Tharaka A

来源：IEEE Transactions on Signal Processing, 2010, 58(11): 5744-5755.

DOI：10.1109/TSP.2010.2057427

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

This paper studies signal concentration in the time and frequency domains using the general constrained variational method of Franks. The minimum kth (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.

• 出版日期2010-11