Interpolation and Extrapolation by Prolate Spheroidal Wave Functions Using Nonuniform Division and Generalized Chirp Modulation

Interpolation and extrapolation are to fill and predict missing values. To perform these works well, the bases that are highly concentrated in the time-frequency plane and match the characteristics of signals should be adopted. In this work, we propose several algorithms to deal with these tasks. Their concepts are based on generalized chirp-modulated and time-frequency division forms of prolate spheroidal wave functions, boasting attracting mathematical properties. Time-frequency divided prolate spheroidal wave functions can well approximate a signal whose energy distributes sparsely in the time-frequency plane. Moreover, generalized chirp modulation can well model a signal whose instantaneous frequency varies with time. Several experiments are conducted and the effectiveness of our proposed algorithms is manifested by the experimental results and quantitative evaluation.