A novel temporal basis function for time domain integral equation solvers

A novel MOT temporal basis function designed for interpolating bandlimited signals, is proposed. The basis function proposed here derives from prolate spheroidal wave functions. It is shown that the interpolation error associated with the use of the proposed function can be made arbitrarily small, and decays exponentially fast as its duration and sampling rate increase. It is observed that for many reasonable choices of their construction parameters, the novel basis functions bear similarities to shifted Lagrange interpolating polynomials. The proposed basis function's principal advantage over shifted Lagrange interpolating polynomials arises in the context of the low-frequency TDIE solvers as the interpolated signals derived from it are automatically bandlimited.