Approximating Signals From Nonuniform Continuous Time Samples at Unknown Locations

Sampling theorems exist to recreate bandlimited signals from both uniform and nonuniformly spaced samples. This is not the case for nonuniform samples when their locations are unknown. This problem has been addressed in the past for discrete-time signals. This correspondence provides an algorithm for finding the sample locations in continuous time by approximating the signal that created the samples with a finite Fourier Series. An example is given that shows the performance of this algorithm. It is a real-world problem of recreating a signal consisting of thousands of samples with unknown locations from a Fourier transform spectrometer (FTS)