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.
Published
2016-08-29
Issue
Section
RESEARCH ARTICLES
© International Society for Neurofeedback and Research (ISNR), all rights reserved. This article (the “Article”) may be accessed online from ISNR at no charge. The Article may be viewed online, stored in electronic or physical form, or archived for research, teaching, and private study purposes. The Article may be archived in public libraries or university libraries at the direction of said public library or university library. Any other reproduction of the Article for redistribution, sale, resale, loan, sublicensing, systematic supply, or other distribution, including both physical and electronic reproduction for such purposes, is expressly forbidden. Preparing or reproducing derivative works of this article is expressly forbidden. ISNR makes no representation or warranty as to the accuracy or completeness of any content in the Article. From 1995 to 2013 the Journal of Neurotherapy was the official publication of ISNR (www. Isnr.org); on April 27, 2016 ISNR acquired the journal from Taylor & Francis Group, LLC. In 2014, ISNR established its official open-access journal NeuroRegulation (ISSN: 2373-0587; www.neuroregulation.org).