An algorithm for spectral analysis of 1/f noise in nonlinear dynamical systems

The indirect time series analysis method is applied to spectral analysis of 1/f noise in one-dimensional discrete dynamical systems. This method is based on approximating the Perron-Frobenius integral operator by a finite dimensional matrix by using the Galerkin method. Numerical examples show that the results are in good agreement with results using the fast-Fourier-transform (FFT) in wide frequency ranges. Both results indicate that the Procaccia-Schuster theoretical result for the spectral power law in the limit of zero frequencies does not apply in wide frequency ranges. This method gives stable and high precision results, while the FFT method gives results with scattered values