Abstract A method to find the ``true'' Fourier spectrum for unevenly spaced time series is developed. It is found that the ``true'' Fourier spectrum associates with the conventional Fourier spectrum by a system of linear equations, so the ``true'' Fourier spectrum can be obtained by any methods of solving the system of linear equations (here the method of iterative process is choosed). It is an effective method for detecting and describing the ``true'' multiperiodic signals, even in the case where some strong peaks in a conventional Fourier spectrum occur at spurious frequencies. For the ``true'' Fourier spectrum composed of finite isolated harmonic components, this method gives a better estimation of the frequencies and amplitudes. This method is tested using simulated time series and the published data for servel blazars. Then it is applied to some radio variabilities of a sample of blazars. In some cases, typical timescales of several decades are found, indicating that this method is capable of finding very low frequency signals.
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