A nonstationary signal analysis technique is introduced, which regards an oscillatory physiological signal as a sum of its fragments, presented in the form of a fragmentary decomposition (FD). The virtue of FD is that it is free of the necessity to choose a priori the basis functions intended for signal analysis or synthesis. FD uses an unchanged signal fragment between adjacent zero-crossings, as a natural basis function called the half-wave function (HWF). To show that such a function is a physically meaningful object, Fourier transform methods were employed, supported by the similar basis function (SBF) algorithm, which provides the means for numerical Fourier transform spectroscopy of separate half-waves and their frequency domain description in terms of both amplitude and phase. The application of this method to parameter identification of 751 EMG half-waves from the eye blink EMG records of ten normal subjects showed that HWF's frequency domain image represents a Gaussian distribution, which applies over a defined range of relative frequencies. This empirical evidence shows that HWFs are produced by a specific system of first-order nonlinear differential equations, whose dependency on a number of random factors is characteristic of deterministic chaos. The particular form of solutions indicates that statistical regularities relevant to the central limit theorem are likely to underlie the genesis of the mass potentials studied. FD shows potential utility in a range of nonstationary physiological signals.