Reconstruction from Unevenly Spaced Sampled Data Using the Iterative Methods

Two iterative algorithms were introduced for reconstructing a band-limited function from its unevenly spaced sampled data. Each iterative method introduces its own varying coefficient which is adaptively determined at each iteration. A varying coefficient for the first algorithm is adaptively determined based on minimizing the error energy of the signal at each iteration. The second method (the method of steepest descent) determines a varying coefficient based on minimizing the error energy reduction of the unevenly spaced sampled data at each iteration. We show that the reconstructed signal from these algorithms converges to the desired signal when the sampling set {tn} is a sequence such that the nonharmonic Fourier functions {exp(jwt n)} form a complete set in the signal subspace of the original signal.