# Fourier Spectral Analysis

Initial Publication Date: December 21, 2006

When students suspect cyclic signals are embedded within their data they can perform a Fourier Spectral Analysis of their data. It is important that they remove any trend in their data before performing the analysis. Most programs take advantage of the Fast Fourier Transform (FFT) Algorithm which requires that data sets must be of specific length (2N

^{2}). Our discussion here assumes that the data is in the form of a time series. However, FFT spectral analysis is also often used on cyclic spatial data.Introductory geoscience students use Excel in the Starting Point Example Graphing Sunspots to graph monthly mean Greenwich sunspot number since 1749 and then use the free software

*Spectra*to perform a Fourier analysis of the sunspot record.There are several links that can help students better understand the link between the time domain and frequency domain. Among these are:

- The FFT Lab from Stanford University. In this interactive applet students can edit the graphs in either the time or frequency domains and see how this influences graphs in the frequency or time domain.

There are many spectral analysis programs/tools available for your students to use. Among these are:
Tools in such common programs as MatLab, Mathematica, IDL, and Maple.
Microsoft Excel has a FFT Add-in Tool.
ClimLab ( This site may be offline. ) is a free software pack offered through Columbia University. It is fairly sophisticated but is user friendly and makes spectral analysis of a single time series very easy.
Free Software at NOAA's NGDC has a Mac OS 9 analysis package that was described in EOS. It is versatile and easy to use.
Spectra is an easy to use free spectral analysis package for your PC.
Singular Spectrum Analysis - MultiTaper Method (SSA-MTM) Toolkit from UCLA is a multiplatform package. The link leads you to information regarding this package including downloads, documentation, and a reprint of a 2001 Reviews of geophysics Article describing the package.
The Graphical Analysis package from Vernier Software (more info) is a low cost (~$80.00) and user friendly graphical package that includes FFT spectral analysis.