Extended Fourier series for time-varying filtering and reconstruction from level-crossing samples

In this paper an extension of the classical Fourier series for analysis of non-stationary signals with time-varying spectral content is presented. This, in comparison to the classical series, allows reducing the number of Fourier coefficients required to represent the signal. The proposed extended Fourier series can be used for time-varying filtering, which in turn can be used for recovery of the signals from level-crossing samples. This has been demonstrated by numerical simulations on different test signals.