Accession Number:

AD0741211

Title:

A Generalization of Harmonic Analysis for Detection of Long-Period Biorhythmicities from Short Records,

Descriptive Note:

Corporate Author:

NAVY MEDICAL NEUROPSYCHIATRIC RESEARCH UNIT SAN DIEGO CALIF

Personal Author(s):

Report Date:

1971-01-01

Pagination or Media Count:

24.0

Abstract:

Successive ordinates of the line spectrum as computed by means of the discrete Fourier transform indicate how the variance of a given time series is apportioned among the members of a set of orthogonal, i.e. harmonic, frequencies. The continuous Fourier transform provides a means of interpolation between these frequencies. However, when the original data include a long-period sinusoid whose frequency is below the fundamental, then neither the discrete nor the continuous Fourier transform gives a good indication of the presence of long-period wave function. The detection and estimation of such a function can be accomplished by a generalization of harmonic analysis along the framework of regression analysis. The procedure computes a squared multiple correlation coefficient corresponding to any frequency, by regressing sine and cosine weights on the observed data. The method and its applications are illustrated by simple numerical examples. Author

Subject Categories:

  • Anatomy and Physiology

Distribution Statement:

APPROVED FOR PUBLIC RELEASE