Local Nonlinear Filtering

Classical methods of filtering time series use Fourier power spectral analysis to separate signals from noise. Improved methods of signal separation can be developed by using projection techniques based on concepts of nonlinear dynamics. However, such methods are limited in their ability to distinguish between dynamically independent signals. Here we show how it is possible to combine Fourier projection with local nonlinear prediction to provide a methodology which can, in principle, recognise independent dynamical signals. We apply the methodology to a variety of chaotic signals with superimposed sine waves, and show how the sine wave frequency can be recognised dynamically (but not spectrally).