• Vleeschouwer, David De
• Claeys, Philippe
• Sinnesael, Matthias
• Zivanovic, Miroslav
• Schoukens, Johan

Abstract

Accuratelydecipheringperiodicvariationsinpaleoclimateproxysignalsisessentialforcyclostratigraphy.Classical spectral analysis often relies on methods based on the (Fast) Fourier Transformation. This techniquehasnouniquesolutionseparatingvariationsinamplitudeandfrequency.Thischaracteristicmakesitdifficulttocorrectlyinterpretaproxy’spowerspectrumortoaccuratelyevaluatesimultaneouschangesinamplitudeand frequency in evolutionary analyses. Here, we circumvent this drawback by using a polynomial approach toestimateinstantaneousamplitudeandfrequencyinorbitalcomponents.Thisapproachhasbeenprovenusefulto characterize audio signals (music and speech), which are non-stationary in nature (Zivanovic and Schoukens,2010, 2012). Paleoclimate proxy signals and audio signals have in nature similar dynamics; the only difference isthe frequency relationship between the different components. A harmonic frequency relationship exists in audiosignals, whereas this relation is non-harmonic in paleoclimate signals. However, the latter difference is irrelevantfor the problem at hand.Usingaslidingwindowapproach,themodelcapturestimevariationsofanorbitalcomponentbymodulat-ing a stationary sinusoid centered at its mean frequency, with a single polynomial. Hence, the parameters thatdetermine the model are the mean frequency of the orbital component and the polynomial coefficients. The firstparameter depends on geologic interpretation, whereas the latter are estimated by means of linear least-squares. Asan output, the model provides the orbital component waveform, either in the depth or time domain. Furthermore,itallowsforauniquedecompositionofthesignalintoitsinstantaneousamplitudeandfrequency.Frequencymodulation patterns can be used to reconstruct changes in accumulation rate, whereas amplitude modulation canbeusedtoreconstructe.g.eccentricity-modulatedprecession.Thetime-variantsinusoidalmodelisappliedtowell-established Pleistocene benthic isotope records to evaluate its performance.<br/><br/>ZivanovicM.andSchoukensJ.(2010)OnThePolynomialApproximationforTime-VariantHarmonicSignal Modeling. IEEE Transactions On Audio, Speech, and Language Processing vol. 19, no. 3, pp. 458–467.Doi: 10.1109/TASL.2010.2049673.ZivanovicM.andSchoukensJ.(2012)SingleandPiecewisePolynomialsforModelingofPitchedSounds.IEEETransactionsOnAudio,Speech,andLanguageProcessingvol.20,no.4,pp.1270–1281.Doi:10.1109/TASL.2011.2174228.

Topics

• impedance spectroscopy
• extraction