Adaptation of Spectral Analysis to Reality

Spectral analysis of on-line measured data by means of real-valued cosine transform within the domain of positive real numbers has not just proven a simpler but quite equivalent alternative as compared to analysis with complex-valued Fourier transform within the domain of all real numbers. It also contrasts by being adequate to reality. Merely arbitrary and redundant data are missing. Notorious as well as unseen pitfalls of complex-valued spectral analysis are prevented from the very beginning. This includes non-causality, apparent symmetry, and a dilemma with unphysical behavior either in frequency domain or in time domain. While complex-valued transform assumes ordinary time, relating to an arbitrarily chosen event, cosine transform may take the opposite point of view, and it refers to the natural zero of elapsed time, permanently sliding relative to all events, as does an also natural gradual horizon of relevance replacing the arbitrary window of time. Since all traditional theories have been based on the ordinary notion of time and on belonging also abstract relationships, adaptation of spectral analysis to the reality of actual process suffers from neglect of its mathematical basis