Signal Extrapolation with Linear Prolate Functions
A simple, efficient and reliable method for bandlimited signal extrapolation valid up to basically an arbitrarily high range of frequencies is proposed. The orthogonal properties of linear prolate functions (LPFs) 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 LPFs, 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 our algorithm for the two sets are discussed in detail. Further comparisons show that the proposed method performs optimally over other recent techniques used. The possibility of using our algorithm for extrapolating real experimental signals is also explored. Though it is not fully usable for extrapolating real signals as such, there were some interesting observations made during this study which could be of some help for the future works in this field.