Manual for the use of the Astronomical Component Estimation Model version 1 (ACE v.1)
(29-04-2016)

Sinnesael, M., Zivanovic, M., De Vleeschouwer, D., Claeys, P., and Schoukens, J.
"Astronomical component estimation (ACE v.1) by time-variant
sinusoidal modeling", submitted to Geoscientific Model Development. 
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GENERAL INFO:

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ACE v.1 is designed in a MATLAB environment. 

It includes two MATLAB functions: 

(1) "OrbitalComponentEstimation"

which estimates waveforms from astronomical components.

(2) "SedimentationRateEstimation"

which estimates the instaneous frequencies and associated sedimentation rates based 
on the output of function (1)

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REQUIRED INPUT DATA:

(1) a nx2 matrix containing the stratigraphic series with in the first column the
m-levels and in the second the data. Uniform sampling is assumed.

This can for example be done by reading a text file into MATLAB

e.g. data = load('datacontainingtextfile.txt');


(2) the ouput of function (1).


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PROVIDED OUTPUT:

The functions are designed to export the raw data (.mat) which then can be used for various
purposes according to the users wish (e.g. plotting).

(1) "EstimatedComponents.mat" wich contains the waveforms of the n estimated components

(2) "InstanteousFrequecyEstimates.mat " wich contains the estimated instaneous frequencies
 of the n estimated components

    "SedimentationRateEstimates.mat" wich contains the estimated sedimentation rates of 
the n estimated components


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DETAILED USERS INSTRUCTIONS:

(1) "OrbitalComponentEstimation"

function OrbitalComponentEstimation(data,Nsources,bands,windowsize,Porder)

% OrbitalComponentEstimation - Extracts principal orbital components from
%   cyclostratigraphic data.
%
% About:
%   This script is part of the complementary material for the manuscript
%   entitled "Astronomical component estimation (ACE v.1) by time-variant
%   sinusoidal modeling", submitted to Geoscientific Model Development.
%
% Input:
%   data              Stratigraphic series: first column should be depth 
%                     (in meters), second column should be data value.
%                     Uniform sampling is assumed.
%   Nsources          Number of orbital components to extract
%   bands             (Nsources x 2)-matrix where each row encompasses
%                     the lower and upper frequency bound (in Hz) for a 
%                     given component.
%                     These frequency ranges can be determined using for
%                     example spectral anlysis (Periodogram, MTM etc.)
%   windowsize        length of the analysis frame in meters
%                     See Chapter 2.3 in Sinnesael et al., 2016, 
%                     Geoscientific Model Development for instructions
%   Porder            number of terms for the polynomial approximation.
%                     See Chapter 2.3 in Sinnesael et al., 2016, 
%                     Geoscientific Model Development for instructions%
%
% Description:
%   Estimates the spatial-domain waveforms of orbital compnents by means of
%   non-stationary polyinomial-based sinusoidal modeling. Key reference: 
%   Zivanovic, M., and Schoukens, J. "On The Polynomial Approximation for 
%   Time-Variant Harmonic Signal Modeling", IEEE Transactions on Audio, 
%   Speech, and Language Processing, 19, 458-467, 2011.
%
% Example:
%   OrbitalComponentEstimation(data,2,[0.01 0.07; 0.18 0.25],80,2)

(2) "SedimentationRateEstimation"

function SedimentationRateEstimation(fileName,windowsize,Porder,Tnominal)

% InstantaneousFrequencyEstimation - Estimates the sedimentation rate from 
% the estimated waveforms of the orbital components. 
%
% About:
%   This script is part of the complementary material for the manuscript
%   entitled "Astronomical component estimation (ACE v.1) by time-variant
%   sinusoidal modeling", submitted to Geoscientific Model Development.
%
% Input:
%   fileName          *.mat file containing the estimated orbital
%                     component waveforms
%   windowsize        length of the analysis frame in meters
%                     See Chapter 2.3 in Sinnesael et al., 2016, 
%                     Geoscientific Model Development for instructions
%   Porder            number of terms for the polynomial approximation.
%                     See Chapter 2.3 in Sinnesael et al., 2016, 
%                     Geoscientific Model Development for instructions%
%   Tnominal          nominal orbital component period in kyr
%                     Predicted periods for precession and obliquity can be
%                     found in Berger et al., (1992) or Laskar et al.,
%                     (2004)
% Description:
%   From spatial-domain waveforms it estimates the instantaneous frequency
%   and sedimentation rate for orbital components.
% Example:
%   SedimentationRateEstimation('EstimatedComponents',60,2,[41 23])

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REFERENCES:

Sinnesael, M., Zivanovic, M., De Vleeschouwer, D., Claeys, P., and Schoukens, J.
"Astronomical component estimation (ACE v.1) by time-variant
sinusoidal modeling", submitted to Geoscientific Model Development. 


Estimates the spatial-domain waveforms of orbital compnents by means of
non-stationary polyinomial-based sinusoidal modeling. Key reference: 

Zivanovic, M., and Schoukens, J. "On The Polynomial Approximation for 
Time-Variant Harmonic Signal Modeling", IEEE Transactions on Audio, 
Speech, and Language Processing, 19, 458-467, 2011.