A little command line tool (macOS only) to perform Taner bandpass filtering and Hilbert transformation.
https://www.rocksolidimages.com/attributes-revisited/#_Toc328470897
Welcome to tanerHilbert Analysis(version 0.0.1, build 2). ©2018 Heiko Pälike Usage: tanerHilbert [options] file file format: tab separated columns, data must be equidistantly spaced. Instead of file can specify '-' for stdin. -h, --help: Displays help message. -l, --lowerFreqLimit: Lower frequency for taner bandpass. Default: 0.0 -u, --upperFreqLimit: Upper frequency for taner bandpass. Default: 0.5 (NYQUIST if deltaT = 1) -l2, --lowerFreqLimit2: Lower frequency for second taner bandpass. Default: 0.0 -u2, --upperFreqLimit2: Upper frequency for second taner bandpass. Default: 0.5 (NYQUIST if deltaT = 1) -r, --rollOver: rollOver. Default: 1e12 roll-off/octave -d, --detrendingOrder: Order for polynomial detrending. 0 removes DC only. >0 removes a polynomial fit. Default: not set -s, --filterAbscissaLower: filter on Abscissa (x-axis) data greater or equal than value specified. -e, --filterAbscissaUpper: filter on Abscissa (x-axis) data lesser or equal than value specified. -z, --columnSeparator: Use this as columns separtor for input file instead of default tab \t. Default: \t -k, --skipHeaderLines: Specify number of (header)lines to be skipped. Default: 0 -a, --abscissaColumn: Specify column number for abscissa (time or depth). Default: 1 -o, --ordinateColumn: Specify column number for ordinate (data). Default: 2 -t, --deltat: Specify time/depth offset between data. Default: 1.0 -O, --timeOrigin: Specify time/depth origin. Default: first time --time_scaling: Specify if time column is in negative days, and convert to kyr. Default: false -n, --decimate: Specify decimation of input data. Default: 1 (take every value) --version: Shows current version and build of this software -v, --verbose: Print verbose messages. Specify multiple times to increase verbosity. --references: Shows references to papers and sources. --licenses: Shows licenses of code components used in this software.
Binary download:
after download, add execute permissions by 'chmod a+x ./tanerHilbert'
Then try it on a sample file La2004_ecc.txt
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Then filter and demodulate again:
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The bottom graph shows the ~2.4 Myr amplitude modulation of the 400kyr modulation of the 100kyr eccentricity component. Top red graph shows instantaneous frequency (would be around 1/2400 = 4.16x10-4 for a 2.4 Myr cycle).
References:
1. Taner (2003): https://www.rocksolidimages.com/attributes-revisited/#_Toc328470897
2. Zeeden, C. et al. (2018), Taner filter settings and automatic correlation optimisation for cyclostratigraphic studies, Computers & Geoscience 119, p. 18-28, doi:10.1016/j.cageo.2018.06.005