1. Geology 491 Spectral Analysis
Filtering the Amplitude Spectrum
tom.h.wilson
Department of Geology and Geography
West Virginia University
Morgantown, WV

2. The slides discussed here are presented in today’s handout
The slides discussed here are presented in today’s handout. Refer to your handout for additional explanation and context.
In class the other day we built or simulated a theoretical climate data response using simple sinusoids to represent the variation of eccentricity, tilt and precession. The data we made up in Excel looked something like that shown at right, although the relative scaling of different astronomical influences differs.
See Figure 12 of your handout

3. After we introduced some noise we ended up with a data set similar to that above right. We took the Fourier transform to get the amplitude spectrum using PsiPlot.
See Figure 13 of your handout

4. Filtering
The plots at right illustrate the design of a “lowpass” filter defined by the red line in the amplitude spectrum.
The effect of bandpass filtering on the temporal response is shown at bottom right. Note that only the longer period variation plus some noise remain after lowpass filtering.
See Figure 14 of your handout

5. The idea of the bandpass filter is illustrated at right
The idea of the bandpass filter is illustrated at right. The bandpass filter passes a range of frequencies extending from some low cut frequency to a high cut frequency.
The bandpass filter at right was designed to extract the precessional variations from the simulated data.
We will talk about smoothing on Thursday, but basically the process of filtering is like taking a weighted moving average.
See Figure 15 of your handout

6. The spectra shown in the lower two plots at right are derived from the theoretical behavior predicted for the combined effects of orbital eccentricity, axial tilt and precession. Note that a variety of peaks appear in the spectrum and not just three we might expect from the popularized discussions of these influences.
See Figure 1 of your handout

7. Next – let’s take a closer look at the amplitude spectra of two of the data sets you are working with. We will work through most of the following in lab today.
See Figure 2 of your handout

8. See Figure 3 of your handout

9. See Figure 4 of your handout

10. See Figure 5 of your handout

11. See Figure 6 of your handout

12. See Figure 7 of your handout

13. See Figure 9 of your handout

14. See Figure 10 of your handout

15. See Figure 11 of your handout

16. Due Date
The filtering lab should be turned in no later than noon of December 4th