Spectral mimicry: A method of synthesizing matching time series with different Fourier spectra

Joel E. Cohen, Charles M. Newman, Adam E. Cohen, Owen L. Petchey, Andrew Gonzalez

Research output: Contribution to journalArticlepeer-review

Abstract

Given a stationary time series X and another stationary time series Y (with a different power spectral density), we describe an algorithm for constructing a stationary time series Z that contains exactly the same values as X permuted in an order such that the power spectral density of Z closely resembles that of Y. We call this method spectral mimicry. We prove (under certain restrictions) that, if the univariate cumulative distribution function (CDF) of X is identical to the CDF of Y, then the power spectral density of Z equals the power spectral density of Y. We also show, for a class of examples, that when the CDFs of X and Y differ modestly, the power spectral density of Z closely approximates the power spectral density of Y. The algorithm, developed to design an experiment in microbial population dynamics, has a variety of other applications.

Original languageEnglish (US)
Pages (from-to)431-442
Number of pages12
JournalCircuits, Systems, and Signal Processing
Volume18
Issue number4
DOIs
StatePublished - 1999

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics

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