IJCsatellite IJCsatellite/physics

physics/0203081 http://arxiv.org/abs/physics/0203081

From: Axel G. Rossberg [view email]
Date (v1): Wed, 27 Mar 2002 17:30:02 GMT   (15kb)
Date (revised v2): Wed, 4 May 2005 14:05:45 GMT   (63kb)

On the limits of spectral methods for frequency estimation

Authors: A. G. Rossberg

Comments: 18 pages, 6 figures (Referee did not like the previous title. Many other changes)
Subj-class: Data Analysis, Statistics and Probability; General Physics; Chaotic Dynamics
Journal-ref: International Journal of Bifurcation and Chaos, 14(6), 2115-2123 (2004)

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.

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