Bandlimited Signal Extrapolation Using Prolate Spheroidal Wave Functions

摘要

A simple, efficient and reliable method to extrapolate bandlimited signals varying from lower to higher frequencies is proposed. The orthogonal properties of linear prolate spheroidal wave functions (PSWFs) are exploited to form an orthogonal basis set needed for synthesis. A significant step in the process is the higher order piecewise polynomial approximation of the overlap integral required for obtaining the expansion coefficients accurately with very high precision. Two sets of PSWFs, one relatively with lower Slepian frequency and the other with higher Slepian frequency, are considered. Numerical results of extrapolation of some standard test signals using the two sets are presented, compared, discussed, and some interesting inferences are made.