Highly accurate reconstruction algorithm for bandwidth-limited signals and application to fringe signal recovery

We present a bandwidth-limited signal reconstruction algorithm with high accuracy as a generalization of the conventional "self-truncating" method by using samples taken at a rate higher than the Nyquist rate. The extra sampling rate enables us to lower the truncation error by applying an appropriate window function that tapers the signal to be approximately limited in both the space and frequency domains up to exponentially small errors. The sampling theorem is used in the frequency domain for a space-limited signal to parameterize the tapered signal in terms of discrete samples in the frequency domain, which are determined by a least-squares fitting to handle both irregularly and regularly sampled data. Error analysis for the Gaussian and Kaiser window functions shows that the upper bounds of the errors for reconstructing the signal near the center of sampling decay exponentially in parameter qN faster than the error upper bound of the conventional "self-truncating" method, where q is the extra sampling rate relative to the Nyquist rate and 2N+1 is the number of samples used. We use simulation data to demonstrate the efficacy of this algorithm in reconstructing the fringe signals, which is crucial for the SIM (Space Interferometry Mission) PlanetQuest instrument calibration.