非負値エルミートテンソルとベクトル時系列(続)

概要

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The present report is continued from a previous paper of the same title published in the last issue of this journal. Evolutionary spectral properties of deterministic and real-valued vectorial time series are now related directly to the energy fed into isotropically multi-D simple oscillators during their complex-valued tensorial formulations. This makes use of quadrature functions by means of Hilbert mapping evaluated for the time series and also for the oscillators' response, and provides an Hermitian extension of the foregoing works by Arias, Husid, Housner-Jennings and the author. A primary interest is taken in how to associate an imaginary-part pair to the evolving tensor of the work transmitted to an oscillator. The findings high-light a complete chain of mathematical relations linking the three complex Hermitian and evolutionary tensors of power spectrum, work done to oscillators and accumulation of squared amplitudes. Derived from the specific viewpoints of dynamics, this can be understood as a generalization of the elementary Parseval's equality.
一般社団法人日本建築学会の論文
1991-03-15