Spectrum Analysis Basic Notation and Principles - Preparing the Data for Analysis
Let us now consider a few other practical points in spectrum analysis. Usually, one wants to subtract the mean from the series, and detrend the series (so that it is stationary) prior to the analysis. Otherwise the periodogram and density spectrum will mostly be "overwhelmed" by a very large value for the first cosine coefficient (for frequency 0.0). In a sense, the mean is a cycle of frequency 0 (zero) per unit time; that is, it is a constant. Similarly, a trend is also of little interest when one wants to uncover the periodicities in the series. In fact, both of those potentially strong effects may mask the more interesting periodicities in the data, and thus both the mean and the trend (linear) should be removed from the series prior to the analysis (by default, they are removed in the Time Series module). Sometimes, it is also useful to smooth the data prior to the analysis, in order to "tame" the random noise that may obscure meaningful periodic cycles in the periodogram.