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

Given a stationary time series X and another stationary time series Y (with a different power spectral density), we describe an algorithm for construc ting 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 rese mbles that of Y. We call this method spectral mimicry. We prove (under cert ain 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 exa mples, that when the CDFs of X and Y differ modestly, the power spectral de nsity of Z closely approximates the power spectral density of Y. The algori thm, developed to design an experiment in microbial population dynamics, ha s a variety of other applications.