摘要
We introduce a family of orthogonal functions,termed as generalized Slepian functions(GSFs),closely related to the time-frequency concentration problem on a unit disk in D.Slepian[19].These functions form a complete orthogonal system in L_(ωα)^(2)(−1,1)with̟ω_(α)(x)=(1−x)^(α),α>−1,and can be viewed as a generalization of the Jacobi polynomials with parameter(α,0).We present various analytic and asymptotic properties of GSFs,and study spectral approximations by such functions.
基金
supported by Singapore AcRF Tier 1 Grant RG58/08,Singapore MOE Grant T207B2202
Singapore NRF2007IDM-IDM002-010.