Exact Fourier transform and interpolation of undersampled shifted autocorrelation functions

Statistics – Computation

Scientific paper

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Astronomical Spectroscopy, Autocorrelation, Computational Astrophysics, Fourier Transformation, Image Processing, Interpolation, Computerized Simulation, Emission Spectra, Interferometry, Precision, Signal To Noise Ratios

Scientific paper

A method is presented which makes it possible to solve the principal difficulties associated with the use of autocorrelation functions. In particular, it is shown that undersampling by a factor of two is possible. This saves both time and memory storage or allows better measurements (with an increase in signal-to-noise ratio or the resolving power), which is especially important in space experiments. A new interpolation formula is derived which recovers identically the autocorrelation function from its samples obtained from the shifted undersampling.

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