Numerical Fourier transform spectroscopy of EEG waveforms using similar basis function algorithm

A review of novel method of numerical Fourier transform spectroscopy of non-stationary signals and its applications to the time-frequency waveforms analysis of the electroencephalogram (EEG). The method uses the similar basis function (SBF) algorithm supported by classical methods of numerical estimation of trigonometric integrals based on the polynomial expansion of the function to be transformed. Previous algorithmic implementations of these computational schemes significantly improved accuracy of spectral measurements, as compared with FFT, in beam relaxation spectroscopy. However, the procedures of polynomial approximation are not supported by effective algorithms and require tedious computations. The essence of the SBF algorithm is that this technique supports digital Fourier transform spectroscopy by effective computational schemes. The algorithm decomposes a polynomial approximating function of a signal into the sum of finite elements with a simple analytical form of the frequency spectrum. This reduces spectral estimation to a number of relatively simple frequency domain transforms. Being applied to the time-frequency analysis of EEG, the method provided means to identify specific analytic forms of monolithic waves both in the frequency and time domains. On this basis the methodology of high resolution fragmentary decomposition (FD) has been designed to represent EEG as a linear aggregation of functionally independent components, with generic mass potential (GMP) being the universal functional element. Application of this method to clinical data from patients with borderline personality disorder (BPD) and schizophrenia illustrates that it improves spectral estimates and hence enables the extraction of additional diagnostic information from EEG records.