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# Michael Schulz: Software

## REDFIT-X: Cross-spectral analysis directly from unevenly spaced time series

The program combines the cross-spectral analysis (as in SPECTRUM) with a Monte-Carlo approach for estimating uncertainties of spectral parameters. The program is based on the Lomb-Scargle Fourier transform for unevenly spaced data in combination with the Welch-Overlapped-Segment-Averaging procedure. REDFIT-X can perform harmonic analysis (detection of periodic signal components embedded in red noise (AR1) as well as cross-spectral analysis (cross-amplitude-, coherency- and phase-spectrum). Cross-spectral analysis does not require a common time axis of the two processed time series.

## REDFIT: Red-noise spectra directly from unevenly spaced time series

Paleoclimatic time series are commonly unevenly spaced in time, making it difficult to obtain an accurate estimate of their typical red-noise spectrum. This Fortran 90 program overcomes this problem by fitting a first-order autoregressive (AR1) process, being characteristic for many climatic processes, directly to unevenly spaced time series. Hence, interpolation in the time domain and its inevitable bias can be avoided. The program can be used to test if peaks in the spectrum of a time series are significant against the red-noise background from an AR1 process.

New in version 3.8: Rare crashes for time series with near-zero persistence and very high time resolution fixed.

New in version 3.7: Automatic check of input data added. If the program encounters decreasing ages it will stop. Identical age entries and the corresponding data values are automatically averaged.

New in version 3.7: Automatic check of input data added. If the program encounters decreasing ages it will stop. Identical age entries and the corresponding data values are automatically averaged.

A

**graphical user interface**is now available for REDFIT. It was developed by Boris Priehs (Univ. Bremen) and uses the commercial software MATLAB (Version 7 or above) to easily control the settings of REDFIT and to visualize the results:## SPECTRUM: Spectral analysis of unevenly spaced time series

A menu-driven PC program that allows the analysis of unevenly spaced time series in the frequency domain. The program is based on the Lomb-Scargle Fourier transform for unevenly spaced data in combination with the Welch-Overlapped-Segment-Averaging procedure. SPECTRUM can perform: 1) harmonic analysis (detection of periodic signal components), 2) spectral analysis of single time series and 3) cross-spectral analysis (cross-amplitude-, coherency- and phase-spectrum). Cross-spectral analysis does not require a common time axis of the two processed time series. 4) Analytical results are supplemented by statistical parameters that allow the evaluation of the results. During the analysis a user is guided by a variety of messages. 5) Results are displayed graphically and can be saved as plain ASCII or PCX files. 6) Additional tools for visualizing time series data and sampling intervals, integrating spectra and measuring phase angles facilitate the analysis. Compared to the widely used Blackman-Tukey approach for spectral analysis of paleoclimatic data, the advantage of SPECTRUM is the avoidance of any interpolation of the time series.

## ENVELOPE: Envelope estimation from unevenly spaced time series

This program estimates temporal changes in amplitude (= signal envelope) and phase of a signal component of given period in a time series. The program can process unevenly spaced input data directly, that is, without the requirement of interpolation.

*New in version 5.3*: Automatic check of input data added. If the program encounters decreasing ages it will stop. Identical age entries and the corresponding data values are automatically averaged.

## TIMEFRQ: Time-frequency analysis of unevenly spaced time series

This program estimates temporal amplitude changes of sinusoidal signal components in a given time series over a prescribed frequency range (spectrogram). The program can process unevenly spaced input data directly, that is, without the requirement of interpolation.

## STATNARY: Mean and variance evolution of unevenly spaced time series

This program estimates the time-dependent mean and variance of a time series using a sliding rectangular window. Temporal changes in mean and variance can be used as a first-order check if a time series is weakly stationary. The estimation of time-dependent mean values is equivalent to a box-car (or running-average) low-pass filter. STATNARY can process unevenly spaced time series directly, that is, without the requirement of interpolation.

## PALEOMAP

Forward and inverse transformation for the polyconical projection used in the 'Atlas of Lithological-Paleogeographical Maps of the World - Mesozoic and Cenozoic of continents and oceans' (Ronov et al., 1989).