4.7.4 Evolutionary Spectral Analysis

This function conducts evolutionary spectral analysis with user-defined parameters.

Steps:

1. Select a data file in the Main Window.

For example, click “Basic Series” – “Examples” – “Late Triassic Wayao gamma ray”.

You will have a data file “Example-WayaoCarnianGR0.txt”.

Let’s use “Math” – “Sort/Unique/Delete-empty” and “Interpolation” tools to ensure the format is supported by Acycle (increasing order and unique sampling rate).

We will have a file “Example-WayaoCarnianGR0-rsp0.2.txt” after interpolation using a 0.2 m sampling rate.

Warning: The data file must be an evenly spaced depth/time series.

2. Select Timeseries --> Evolutionary Spectral Analysis menu

3. Select Method.

• The default method is the Fast Fourier transform (LAH) by Linda A. Hinnov (Kodama and Hinnov, 2015).

Other options are

• MatLab’s Fast Fourier transform,

• multi-taper method (MTM) (Thomson, 1982), and

• Lomb-Scargle spectrum (Lomb, 1976; Scargle, 1982).

4. Input for evolutionary spectral analysis panel includes settings for plot frequencies.

Default values from 0 to Nyquist (fnyq = 1 / (N * Δt)), where N is the total number of data, and Δt is the sampling rate.

5. Step of sliding windows

The default value should be sufficient for most paleoclimate projects. The unit may be m, kyr, etc.

6. Sliding Window

The length of the sliding window is very important!

The default value is 35% of the total length of the selected data.

You may need to change this based on the following tips.

Tips: assuming the data series is dominated by 35 m cycles, the window may be 2-4 times of 35 m, that is, 70 to 140 m. A large window can smooth out the higher frequencies signals while a small window cannot detect low-frequency signals.

7. Do you want to show the time series and 2π MTM power spectrum with robust red noise model simultaneously?

See “spectral analysis” part for more explanations of the red noise model.

8. Plot-dimension

2D or 3D with rotation option.

9. Flip Y-axis

give me a try.

10. Time domain zero padding

This option will zero pad the data series at both ends. Resulted evolutionary power spectra will show the missed half-window in typical evolutionary spectra. This newly added option is to add back the missed half-window due to the sliding window methods.

However, this might introduce additional incorrect frequencies (for example, a series with the trend at one or both ends).

11. Colormap

Style can be modified and grid levels can be set (empty value results in a smoothed figure).

12. OK button

generates a new figure showing the evolutionary spectral analysis results. No new files generated automatically.

Shortcut keys

• [Mac]: ⌘ + E
• [Windows]: Ctrl + E

Evolutionary FFT of the Wayao Gamma ray data using a 70 m sliding window and 0.212 m step shown with data series and 2 pi MTM power spectrum

EvoFFT plot only

Evolutionary FFT of the La2004 astronomical solutions using a 400 kyr sliding window and 2 kyr step