How can spectral analysis be performed on very small data sets?

I work as a student in a research lab collecting data from in vitro muscle force measurements. Sometimes we can collect only a small number of force measurements because the muscle does not remain viable for very long. Sometimes the peak force varies in a curious way, and the Professor hopes we might find a pattern in this variation because it might reveal more information on the mechanisms of the muscle cell.

The Professor says we might be able to perform some spectral analysis even though there are only 16 data points. He said that scientists who analyze earthquake data know how to deal with such small data sets. Searching Google for "spectrum analysis small data set matlab" yielded only a couple of results that could be useful. One is "Non-parametric eigenanalysis frequency estimation" and the other is "Maximum entropy method."

Can anyone recommend either of these methods (or something completely different) when trying to find a pattern in the data using such a small number of data points? A book recommendation would be wonderful. Thank you for your advice!