Fourier analysis

Because of its universal relevance, it is recommended to always start the analysis by computing the power spectrum. However, since the power spectrum is not the optimal method for quite a number of TSA applications, other methods should always be tried thereafter.

POWER/TSA -

Power spectrum: This command computes the discrete power spectrum for unevenly sampled data a by relatively slow method. The discrete Fourier power spectrum (cf., e.g., Deeming, 1975) corresponds to a pure sinewave model and has basic significance in time series analysis. The corresponding test statistic is $S(\nu) = \vert{\cal F}X^{(m)}\vert^2$. Because the statistic is the sum of the squares of two generally correlated variables for sine and cosine, it has has no known statistical properties. Therefore, we recommend to use other statistics for a more reliable signal detection and evaluation.

One of the important applications of the power spectrum analysis is the computation of the window function in order to evaluate the sampling pattern. For this particular application, set all data values in column :VALUE to 1 (for instance by using COMPUTE/TABLE) and then apply POWER/TSA. The resulting power spectrum is the window function of the data set.