A fast discrete Fourier transform with unequally-spaced frequencies

Realization of the discrete Fourier transform (DFT) as the fast Fourier transform (FFT) has a widespread application in practice. There are, however, such problems in technology where the application of the FFT method does not justify satisfactory results. Such problems comprise e.g. the analysis of short sections of fast decaying vibrations or the analysis of instantaneous values of nonstationary signal parameters. Solving the problems arising in this type of signals analysis has contributed to development of the algorithm of the DFT fast computing for transient vibrations. The developed method enables one to obtain high resolution for low frequencies by increasing the density of sampling of the analyzed signal. The algorithm in terms of the computer program (Lenort (1989)) has been tested both on the model data and on the real signal records.