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

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.