## 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 language | English (US) |
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Pages (from-to) | 431-442 |

Number of pages | 12 |

Journal | Circuits, Systems, and Signal Processing |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - 1999 |

## ASJC Scopus subject areas

- Signal Processing
- Applied Mathematics