Transforms and Calculations: Behind the Mathematics of Psychophysiology

Abstract

There are numerous scholarly documents with accurate and thorough explanations of the basis of the mathematical processes that have become essential to the field of psychophysiology. Review of many of these has revealed a pervasive emphasis on the technical and theoretical aspects of these formulae and theories with little or no emphasis on the primary and basic understanding of their development and application. This article specifically bridges the gap between the introduction of several cogent mathematical concepts and their ultimate applications within the field of applied psychophysiology, biofeedback, and neurofeedback. Special attention is given to the distinction between transforms and calculations and some of the statistical methods used to analyze them. Because the focus of this article is to enhance conceptual comprehension, integral, differential, and matrix mathematics are not referenced in any of the examples or explanations with the primary reliance on some algebra with verbal and pictorial descriptions of the processes. We suggest a comparison to an overuse of the black box model in which only the input and output are essential. Taking these processes out of the black box encourages the creative application of these mathematical principles as valuable tools for clinicians and researchers. Structured explanations emphasize the relevance of such important concepts as aliasing, autospectrum, coherence, common mode rejection, comodulation, cross spectral density, distribution, Fast Fourier Transform, phase synchrony, significance, standard deviation, statistical error, transform, t test, variance, and Z scores. The objective for providing these clarifications is to enhance the utility of these concepts.