# Person: Zivanovic, Miroslav

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Zivanovic

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Miroslav

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Ingeniería Eléctrica, Electrónica y de Comunicación

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ISC. Institute of Smart Cities

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0000-0001-8729-6657

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1948

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Publication Open Access A decomposition approach to cyclostratigraphic signal processing(Elsevier, 2022) Wouters, Sebastien; Crucifix, Michel; Sinnesael, Matthias; Silva, Anne-Christine da; Zeeden, Christian; Zivanovic, Miroslav; Boulvain, Frédéric; Devleeschouwer, Xabier; Ingeniería Eléctrica, Electrónica y de Comunicación; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio IngeniaritzarenShow more Sedimentary rocks can record signals produced byhighly complex processes. These signals are generated by a progressive deposition of sediments which can be affected, mainly through the climate system, by regular astronomical cycles (i.e. Milankovitch cycles), and by irregular oscillations like the El Niño-Southern Oscillation. Also, usually through biological, chemical and/or physical post-depositional processes,thesedimentary records can be affected by pattern-creating heterogeneous processes. The noise in the signals further complicates the records,and the deposition rate (or sedimentation rate) can fluctuate, which greatly reduces the effectiveness of the classical stationary time-series analysis methods commonly used in cyclostratigraphy (i.e.the study of the cycles found inthe sedimentary records). Faced with this multiplicity of processes, a common approach used in cyclostratigraphy is to reduce each signal to more manageable sub-signals, either over a given range of frequencies (e.g.,by filtering), or by considering a continuum of constant frequencies (e.g.,using transforms). This makes it possible to focus on the features of interest, commonly astronomical cycles. However, working with sub-signals is not trivial. Firstly, sub-signals have a certain amount of cross-cancellation when they are summed back to reconstructthe initial signal. This means that in filters and in transforms, wiggles that are not present in the initial signal can appear in the sub-signals. Secondly, the sub-signals considered often cannot be summed to reconstruct the initial signal: this means that there are processes affecting the signal which remain unstudied. It is possible to takecross-cancellation into accountand to consider the entire content of a signal by dividing the signal into a decomposition: a set of sub-signals that can be added back together to reconstruct the original signal. We discusshere how to reframe commonly used time-series analysis techniques in the context of decomposition, how they are affected by cross-cancellation, and how adequate they are for comprehending the whole signals. We also show that decomposition can be carried out by non-stationary time-series methods, which can mini misecross-cancellation, and have now reached sufficient maturity to tackle sedimentary records signals. We present novel tools to adapt non-stationary decomposition for cyclostratigraphic purposes, based on the concepts of Empirical Mode Decomposition (EMD) and Instantaneous Frequency (IF), mainly: (1) afast Ensemble Empirical Mode Decomposition (EEMD) algorithm, (2) quality metrics for decomposition, and (3) plots to visualise instantaneous frequency, amplitude and frequency ratio. We illustrate the use of these tolos by applying them on a grey scale signal from the site of the Ocean Drilling Program, at Ceara Rise (western equatorial Atlantic), especially to identifyand characterisethe expression of astronomical cycles. The main goal is to show that by minimising cross-cancellation, we can apply in real signalswhat we call the wiggle-in-signal approach: making the sub-signals in the decomposition more representative of the expression, wiggle by wiggle, of all the processes affecting the signal(e.g., astronomical cycles). We finally argue that decomposition could be used as a practical standard output for time-series analysis interpretation of cyclostratigraphic signals.Show more Publication Open Access Astronomical component estimation (ACE v.1) by time-variant sinusoidal modeling(Copernicus Publications, 2016) Sinnesael, Matthias; Zivanovic, Miroslav; Vleeschouwer, David De; Claeys, Philippe; Schoukens, Johan; Ingeniería Eléctrica y Electrónica; Ingeniaritza Elektrikoa eta ElektronikoaShow more Accurately deciphering periodic variations in paleoclimate proxy signals is essential for cyclostratigraphy. Classical spectral analysis often relies on methods based on (fast) Fourier transformation. This technique has no unique solution separating variations in amplitude and frequency. This characteristic can make it difficult to correctly interpret a proxy's power spectrum or to accurately evaluate simultaneous changes in amplitude and frequency in evolutionary analyses. This drawback is circumvented by using a polynomial approach to estimate instantaneous amplitude and frequency in orbital components. This approach was proven useful to characterize audio signals (music and speech), which are non-stationary in nature. Paleoclimate proxy signals and audio signals share similar dynamics; the only difference is the frequency relationship between the different components. A harmonic-frequency relationship exists in audio signals, whereas this relation is non-harmonic in paleoclimate signals. However, this difference is irrelevant for the problem of separating simultaneous changes in amplitude and frequency. Using an approach with overlapping analysis frames, the model (Astronomical Component Estimation, version 1: ACE v.1) captures time variations of an orbital component by modulating a stationary sinusoid centered at its mean frequency, with a single polynomial. Hence, the parameters that determine the model are the mean frequency of the orbital component and the polynomial coefficients. The first parameter depends on geologic interpretations, whereas the latter are estimated by means of linear least-squares. As output, the model provides the orbital component waveform, either in the depth or time domain. Uncertainty analyses of the model estimates are performed using Monte Carlo simulations. Furthermore, it allows for a unique decomposition of the signal into its instantaneous amplitude and frequency. Frequency modulation patterns reconstruct changes in accumulation rate, whereas amplitude modulation identifies eccentricity-modulated precession. The functioning of the time-variant sinusoidal model is illustrated and validated using a synthetic insolation signal. The new modeling approach is tested on two case studies: (1) a Pliocene–Pleistocene benthic δ18O record from Ocean Drilling Program (ODP) Site 846 and (2) a Danian magnetic susceptibility record from the Contessa Highway section, Gubbio, Italy.Show more