Fourier (Spectral) Analysis - Advanced Tab

Select the Advanced tab of the  Fourier (Spectral) Analysis dialog box to access the options described here.

Element Name Description
Single series Fourier analysis Click the Single series Fourier analysis button to perform a spectrum analysis for the currently highlighted variable (series) and then display the Single Series Fourier (Spectral) Analysis Results dialog box. If selected, the transformations specified in the Transformation of input series group box (see below) will be performed prior to the analysis.
Two series Fourier analysis (select dependent var) Click the Two series Fourier analysis button to perform a cross-spectrum analysis of the currently highlighted variable (series) and another variable (selected via Dependent variable, see below). The currently highlighted variable will be treated as the independent or x variable in the analyses. Then, the Single Series Fourier (Spectral) Analysis Results dialog box will be displayed.
Dependent variable Click the Dependent variable button to display a standard variable selection dialog, in which you specify the dependent variable for the Two series Fourier analysis (see above).
Transformation of input series The transformations selected in the Transformation of input series group box are performed on the series prior to the analysis. See Single Spectrum (Fourier) Analysis for a discussion of the process of tapering and the reasons for de-meaning/trending the data.
Taper The so-called process of split-cosine-bell tapering is a recommended transformation of the series prior to the spectrum analysis. It usually leads to a reduction of leakage in the spectral density plots. (Leakage describes the condition when a strong periodicity at a particular frequency results in large spectral density estimates in several adjacent frequencies). The rationale for this transformation is explained in detail in Bloomfield (1976, p. 80-94), see also Tapering.
Subtract mean If you select the Subtract mean check box, then the overall mean is subtracted from the series prior to the analysis. Because the goal of spectrum analysis is to detect underlying periodicity, the overall mean is usually not of interest. If the mean is not removed, then it will "show up" as the cosine coefficient at frequency 0 (zero; the mean can be thought of as a periodic cycle with a frequency of 0 per unit time). Often, this will lead to an extremely large periodogram value at that frequency, which makes it hard to identify other spikes in the periodogram or spectral density plots.
Detrend If you select the Detrend check box, then the linear trend is removed from the series prior to the analysis. Like the mean, an overall trend is not of interest when you want to uncover periodicities in the series. Therefore, it should be removed prior to the analysis.
Other transformations & plots Click the Other transformations & plots button to display the Transformations of Variables dialog box, in which you can perform a wide variety of transformations on the data. The transformed series will be appended to the active work area.
Padding of input series Use the Padding of input series group box to select padding options. You may choose to pad the series prior to the analysis, that is, to add zeros to the end of the series. Padding of the input series may be useful for two reasons: First, in a sense, it allows you to apply a finer "frequency roster" to the series, checking for successive frequencies at smaller increments. Second, for moderate to large size series (e.g., with more than 100,000 cases), choosing to pad (or truncate) the length of the series to a power of 2 may substantially reduce memory requirements and increase speed (for small series, you will not notice any difference). Both of these issues are also discussed in the Single Spectrum (Fourier) Analysis Overview. If extensive padding is used, we recommend that you also taper the series.
Do not pad series; use exact length If the Do not pad series; use exact length option button is selected, then the series will not be padded, and the resulting periodogram will show values for N/2+1 distinct frequencies (where N is the even number of cases in the series). As described in the Overview, the standard (and most efficient) FFT (fast Fourier transform) algorithm requires that the length of the input series is a power of 2. If this is not the case, then 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.
Pad the end of the series with N zeros If you select the Pad the end of the series with N zeros option button, then N zeros will be added to the end of the input series (where N is the number of observations in the input series). Enter the value of N in the N= box. Note that the zeros will be added after the series has been de-meaned/trended (see above).
Truncate length to a power of 2 If you select the Truncate length to a power of 2 option button, then the length of the input series will be truncated so that the number of observations will be equal to a power of 2 (e.g., 8, 16, 32, 64, 128, ...). When the length of the input series is a power of 2, then the so-called fast Fourier transform (FFT) algorithm (widely popularized by Cooley and Tukey, 1965; for various refinements and improvements see Monro, 1975) can be used for the analysis. This is the fastest method for computing the spectrum analysis (the processing time is proportional to N * log2(N).
Pad length to a power of 2 If you select the Pad length to a power of 2 option button, then the length of the input series will be padded with 0s (zeros) so that the number of observations will be equal to a power of 2 (e.g., 8, 16, 32, 64, 128, ...). When the length of the input series is a power of 2, then the so-called fast Fourier transform algorithm (widely popularized by Cooley and Tukey, 1965; for various refinements and improvements, see Monro, 1975) can be used for the analysis. This is the fastest method for computing the spectrum analysis (the processing time is proportional to N * log2(N)).