Adaptive decomposition of band-limited signals using the Fourier transform band-pass filter
In this work theoretical aspects of adaptive decomposition of integrable or square integrable band-limited functions into a finite number of additive components using the Fourier Transform Band-Pass Filter concept are presented. The spectral domain supports of the components are contained in finite intervals selected by adaptive segmentation of the spectral domain support of the analyzed function. Selection of these intervals can be based on prior knowledge about the spectral characteristics of the function. Spectral domain and time domain formulae for the relevant components are derived which enable numerical implementation of the decomposition in the case when time series of function measurements are available.