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

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Abstract

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

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Authors and Affiliations

  1. Rockefeller University, 1230 York Avenue, 10021-6399, New York, New York

    Joel E. Cohen

  2. Columbia University, 10027, New York, New York

    Joel E. Cohen

  3. Centre for Population Biology, Imperial College at Silwood Park, SL5 7PY, Ascot, Berks, UK

    Joel E. Cohen, Adam E. Cohen, Owen L. Petchey & Andrew Gonzalez

  4. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, New York

    Charles M. Newman

  5. Harvard University, 02138, Cambridge, Massachusetts

    Adam E. Cohen

Authors
  1. Joel E. Cohen
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  2. Charles M. Newman
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  3. Adam E. Cohen
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  4. Owen L. Petchey
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  5. Andrew Gonzalez
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Additional information

The work of J. E. Cohen was supported by U.S. National Science Foundation grant BSR92-07293. The research of C. M. Newman was supported in part by NSA Grant MDA 904-96-I-0033 and by NSF Grants DMS-95-00868 and DMS-98-03267. The work of O. L. Petchey and A. Gonzalez was supported by the U.K. Natural Environment Research Council.

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Cohen, J.E., Newman, C.M., Cohen, A.E. et al. Spectral mimicry: A method of synthesizing matching time series with different Fourier spectra. Circuits Systems and Signal Process 18, 431–442 (1999). https://doi.org/10.1007/BF01200792

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  • DOI: https://doi.org/10.1007/BF01200792

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