Anharmonic frequency analysis: the complement to Fourier analysis

Fourier analysis of a finite time series allocates amplitudes and phases to a given set of frequencies which are integer multiples of a basic frequency determined by the length of the time series. Anharmonic frequency analysis (Afa)collects the spectral components between those frequencies and the results are the average amplitude and phase for each band defined by two consecutive frequencies. A repetition of the transform involved for a later reference time determines the effective frequency within each band by the time change of the phase. This process is by far superior to Fourier analysis especially if unknown discrete frequencies are present in the time series and those frequencies are not harmonics of one common basic frequency. The principles of this method, some of its properties and a few results are presented.