Power spectral analysis of continuous text strings

Abstract

The present study aims at evaluating structures and transfer in text strings. 42 text strings written by (younger and older) and 22 text strings written by adults (scientists newspapers and childrens books) were analysed in three ways. Firstly by simple statistical means, secondly by a time series analysis based on Fourier analysis and thirdly by a pattern evaluation analysis based on the Fast Fourier Transform, all three methods having been developed for this analysis. The analysis involving simple statistical means was based on my discovery that the distribution of ‘new’ words along any natural text string is one of exponential ‘decay’. In a double-logarithmic coordinate system each text string can be represented by a straight line determined by the two parameters: intercept A and gradient B, both a function of how fast the vocabulary becomes exhausted as the string is extended. The numerical values of A and B were established for all the text strings, before and after permutation of the strings caused intercept A to increase and gradient B to decrease significantly thus indicating that A is invertedly, B directly related to sequential structure. The analyses established that adult text strings have a higher level of sequential structure than do childrens strings and that amongst adults, popular newspapers have the highest level of structure as well as the highest vocabulary. A computer model (the ’model of best fit’) of a language perception was created in which the sememe evaluation and information transfer of the human’ linguistic device’ – two features which are not easily simulated by a computer – is instead represented by one procedure which lends itself to computer processing and numerical analysis. In this model each incoming word is checked against a ‘reference field’ and sememe evaluation and information transfer are seen in terms of length of text string between reappearances of words. Before the text strings of this study were subjected to power spectral analysis, they were processed by this ‘model of best fid’.

The two different methods of Fourier analysis gave virtually identical power spectra when applied to the same text strings. The Mean Power Density (MPD) and the Variance (CH12) were measured from the power spectra of 25 of the childrens text strings and all 22 adult text strings. Although only by a small amount, MPD’s were consistently higher for adults than for children, confirming earlier findings that adult strings have a higher sequential structure than childrens strings, although the significance level did not quite make it to the 5% level. CH12 of the spectra turned out to be much more significantly correlated with age and language development than was vocabulary and gradient B earlier. The ‘reference field’, defined in the study, was the parameter with the highest correlation with language development. The popular press had the highest MPD, CH12 and ‘reference field’ of all text strings. Both MPD and CH12 decreased with permutation although only the difference with regard to CH12 was significant. Both emission and absorption features were present in all the power spectra. It was suggested that these features represent generative and filter (lexical) functions of the ‘lin-guistic device’. The position of two of the peaks in the power spectra were shown to be common to most of the spectra. These were F=0.484 in the childrens spectra and F=0,375 in the adults’ spectra. Finally it was shown that when a grammatical category (eg. Nouns) were weighted in different text strings, the same peak(s) appeared at about the same frequency in the different spectra, suggesting that identical, grammar specific, generatore and filter functions were involved in the generation of the different text strings.