On non uniform sampling of signals

In a variety of applications, it is desirable to represent a signal by a set of nonuniformly distributed samples. In particular, this is of interest in the case of nonbandlimited signals where an alternative method to uniform sampling is required. In this work, a new approach to nonuniform sampling is introduced and discussed. The proposed method is based on estimation of a time distortion transformation, under which the original signal becomes practically bandlimited and can thus be reconstructed. The time distortion transformation is estimated using an iterative algorithm. According to this approach, the distortion function is accumulated where each iteration is aimed at compensating for differences in the instantaneous bandwidth after the previous iteration. This process converges and reaches a stage where the signal has practically a constant instantaneous bandwidth over the distorted time axis. Due to the iterative nature of the estimation process, most available techniques of localized bandwidth approximation may be used. The resultant mapping can be considered also as a new means for the definition of local bandwidth.