4.7 Amplitude Modulation

How to calculate the amplitude modulation of a time series?

Here is an example showing how to calculate the amplitude modulation of the obliquity solution from the La2004 astronomical solution.

Step 1. Generate obliquity solution

"Basic Series" -> "Astronomical Solution" ->

Select La2004 Astronomical solution, obliquity astronomical parameters, Time interval from 1 k.a. to 10000 k.a.

In the main window of Acycle, you will get a text file entitled

"La2004-Obliquity-1-10000.txt".

Step 2. Remove the mean value of the obliquity solution

Select the above text file, choose "Timeseries" -> "Detrending" tool

Tick the "Mean" checkbox and click **OK**, then "Select & Save detrending Model", choose **Mean (Thick black)** option.

In the main window of Acycle, you will have two text files entitled

"La2004-Obliquity-1-10000-demean.txt" (de-mean data) and

"La2004-Obliquity-1-10000-mean.txt" (mean value).

Step 3. Amplitude Modulation

Select the demean text file "La2004-Obliquity-1-10000-demean.txt", click to choose "Timeseries" -> "Amplitude Modulation" tool.

In the main window of Acycle, you will have two new files entitled

"La2004-Obliquity-1-10000-demean.txt-AM.txt" (amplitude modulation) and

"La2004-Obliquity-1-10000-demean.txt-AMf.txt" (Taner-hilbert filter output)

Step 4. More analyses

You could explore more using the "La2004-Obliquity-1-10000-demean.txt-AM.txt" (amplitude modulation) file.

Detrending, power spectral analysis, evolutionary power spectral analysis, and wavelet transform, etc.