23 同一の振幅スペクトルを有する離散有限時系列の多様性の範囲

概要

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Remarkable limitations and regularities are found for the varieties of discrete and finite time-series having an identical expression of Fourier modulus spectrum. Except for trivial additional factors of time shift and overall sign, the family consists of 2^N solutions where (N+1) stands for the sample size of discretized time function. Furthermore each array of time-axis data can be straightforwardly determined by means of a completely systematic combinatorial treatment of all the roots of an algebraic equation of degree N corresponding to the original array specified. As related to location transfer of zero points on the complex frequency plane with the Fourier amplitudes left unchanged, the current presentation also includes a self-contained set of various mathematical formulas, such as extended appearances of Bode-type integral, associated arithmetic transformations of discrete time-axis array, and features observed in the change of spectral phase properties.
一般社団法人日本建築学会の論文
2005-03-20