Information decomposition of symbolical sequences

Earlier comprehensive mathematical methods were developed for the study of periodicity of continuous and discrete numerical sequences, using Fourier transformation and allowing the definition of the spectral density of a numerical sequence. However, such an application of a Fourier transform demands presentation of a symbolic sequence as a numerical sequence in which the properties of any symbolic text should be displayed unequivocally. The most widely used is the method, including construction from the given symbolic sequence of m symbols consisting of numbers zero and one, and formed according to the law: x(i,j)=1, if the symbol ai occupies a site j, and x(i,j)=0 in all other cases. Here A={a1, a2, ..., am} is the alphabet of a symbolical sequence and m is the size of the alphabet of a symbolical sequence. Then the Fourier transformation is applied to each of the numerical sequences and the Fourier-harmonics are calculated, corresponding to i-type symbols, as well as to matrix structural factors, corresponding to pair correlation of symbols.