Fast filter for unevenly spaced data with application to altimetry

An efficient algorithm for analysing unevenly spaced data using Fast Fourier Transforms (FFT) is presented. The FFT is computed using a method developed by Press and Rybicki (1989) whereby the original data set is replaced by an expanded evenly spaced array with a number of points equal to a power of 2, which produces a spectrum equivalent to the spectrum of the original data. The transformation between the original and the expanded data set is done through a process called “extirpolation”, similar to an inverse Lagrange interpolation. Using this technique a complete filtering algorithm was built. The main innovation introduced is the recovery of the lowest frequencies of the original data set by a process which inverts the “extirpolation” process. The recovered data set is a smoothed version of the original, after removal of the highest frequencies by applying an appropriate cut-off frequency