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

Liying Wei, Rodney A. Kennedy, Tharaka A. Lamahewa
2010 IEEE Transactions on Signal Processing  
This paper studies signal concentration in the time and frequency domains using the general constrained variational method of Franks. The minimum th moment time-duration measure for band-limited signals is formulated. A complete, orthonormal set of band-limited functions in 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
more » ... WF); 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. Index Terms-Fraction out-of-band energy (FOBE), Gabor's function, orthonormal basis, prolate spheroidal wave function (PSWF), time-frequency.
doi:10.1109/tsp.2010.2057427 fatcat:qyffii2bjjdzpicutck4pjttze