Coincident Frequencies and Relative Phases Among Female-Brain Signals and Progesterone-Estrogen levels

Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology provide information, according with their frequency range, of the well known brain signals Delta, Theta, Alpha 1, Alpha 2, Beta 1 and Beta 2 furnishing experts with electroencephalographic (EEG) profile of clinical use obtained from these short periods 5,6. For long periods, an analogous novel procedure is established as follows: Assigning certain numerical value, i.e., the absolute power, to each brain signal at certain sampling times, generates data that can be interpolated and extrapolated through a long period, yielding an absolute power function of time for each signal 7. A further Fourier transform is then performed8,9, to analyze these new functions, finding typical frequencies and their corresponding periods for each one of these signals and, also, relative phases for coincident periods between two or more signals. Our procedure of analysis presented here can be applied, in principle, to any biological signal of interest.