Approximating bandlimited signals associated with the LCT domain from nonuniform samples at unknown locations

The sampling theory describes ways of reconstructing signals from their uniform or nonuniform samples associated with the traditional Fourier transform (FT). Most of the published papers about the sampling theory require signals to be bandlimited in the FT domain and assume that the sample locations and the band width are all known. However, the sample locations are not always known and most of the signals are non-stationary in practical applications. In order to overcome these shortcomings, this paper provides an algorithm for approximating signals from nonuniform samples at unknown locations. These signals are not necessarily bandlimited in the FT domain, however bandlimited in the LCT domain. The experimental results are given to verify the accuracy of the algorithm.