Fast Fourier Transforms (FFT) - Computation of FFT in Time Series
The implementation of the FFT algorithm in the Time Series module allows you to take full advantage of the savings afforded by this algorithm. On most standard computers, series with over 100,000 cases can easily be analyzed. However, there are a few things to remember when analyzing series of that size.
As mentioned above, the standard (and most efficient) FFT algorithm requires that the length of the input series is equal to a power of 2. If this is not the case, additional computations have to be performed. The Time Series module uses the simple explicit computational formulas as long as the input series is relatively small, and the number of computations can be performed in a relatively short amount of time. For long time series, in order to still utilize the FFT algorithm, an implementation of the general approach described by Monro and Branch (1976) is used. This method requires significantly more storage space, however, series of considerable length can still be analyzed very quickly, even if the number of observations is not equal to a power of 2.
For time series of lengths not equal to a power of 2, we would like to make the following recommendations: If the input series is small to moderately sized (e.g., only a few thousand cases), then do not worry. The analysis will typically only take a few seconds anyway. In order to analyze moderately large and large series (e.g., over 100,000 cases), pad the series to a power of 2 (select the respective option in the Padding of input series group box on the Advanced tab of the Fourier (Spectral) Analysis dialog) and then Taper the series during the exploratory part of your data analysis. If necessary, you can later select the Do not pad series, use exact length check box on the Advanced tab of the Fourier (Spectral) Analysis dialog to derive the final estimates.