Reconstruction of nonuniformly sampled bandlimited signals using time-varying discrete-time FIR filters

This paper deals with reconstruction of nonuniformly sampled bandlimited continuous-time signals using time-varying discrete-time FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are known. Under these assumptions, a representation of the reconstructed sequence is derived that utilizes a time-frequency function. This representation enables a proper utilization of the oversampling and reduces the reconstruction problem to a design problem that resembles an ordinary filter design problem. Furthermore, for an important special case, corresponding to a certain type of periodic nonuniform sampling, it is shown that the reconstruction problem can be posed as a filter-bank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions.