A new fast fourier method for evaluating fourier spectra at arbitrary frequencies

This paper deals with some recent problems of frequency determination in dynamical systems. As a main result a new Fast Fourier Transform (FIT) method, the High Resolution Fast Fourier Transform (HRFFT) is presented, which allows for economic evaluation of discrete Fourier spectra at arbitrary frequencies, not just at the evenly spaced points of the rigid frequency grid the ordinary FFT is restricted to (continuous evaluation). Comparison is made to existing methods in what regards continuous evaluation, computational speed, memory requirements and precision, evidencing the high efficiency of the HRFFT. Possible applications of the new technique are indicated, showing that existing methods, as e.g. that of Laskar (1990, Icarus 88) and its extension by idlichovský and Nesvorný (1996, this volume), may strongly benefit from the HRFFT.