Question: We want to use SPSS to compare two groups (2 independent samples t-test). The first group contains real data, the other group is fictional. This fictional group should contain as many "subjects" as the real (1st) group. But the mean is set to 0 and the standard deviation to 1 (standard normal distribution).

There are several [tools](http://in-silico.net/tools/statistics/ttest/) out there to compare two groups by adding the number of subjects, mean and std for every group independently. But how can we do this in SPSS? I only know how to test one variable (group1) against a test value (T=0).

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*EDIT:*
Here a more detailed description of why I wanted to use this two-sample t-test, although this kind of approach seemed strange to me in the beginning. The thing is that we investigated 20 patients and compared their data with a large database of healthy control subjects. That means we did a z-transformation using the reference database (standard procedure in this field (quantitative sensory testing,QST)). 

There are other research groups which suggest to then use the 2-sample t-test I mentioned below, because it would be inappropriate to compare data of 20 patients with data of 1200 controls. So they invented a fictional group with M = 0 and SD = 1 and tested the real data against this fictional data (on a website like [this](http://in-silico.net/tools/statistics/ttest/) --> but Two-Sample T-Test). This approach would be more conservative than using the one-sample t-test with test value=0.

To be honest, I have no idea if this is the right approach. My first idea was to do a one-sample t-test and test the patient group (i.e. their z-values) against the value 0 to see, whether the z-values differ significantly from 0 instead of using a fictional dataset.

Answer: 
Spectral coherence, if used correctly would do it. Coherence is computed at each frequency-and hence is a vector. Hence, a sum of a weighted coherence would be a good measure. You would typically want to weight the coherences at frequencies that have a high energy in the power spectral density. That way, you would be measuring the similarities at the frequencies that dominate the time series instead of weighting the coherence with a large weight, when the content of that frequency in the time series is negligible.

So, in simple words- the basic idea is to find the frequencies at which the amplitude(energy) in the signals are high(interpret as the frequencies that dominantly constitute each signal) and then to compare the similarities at these frequencies with a higher weight and compare the signals at the rest of the frequencies with a lower weight.

The area which deals with questions of this kind is called cross-spectral analysis.
<http://www.atmos.washington.edu/~dennis/552_Notes_6c.pdf> is an excellent introduction to cross-spectral analysis.

Optimal Lag:
Also look at my answer over here: [How to correlate two time series, with possible time differences](https://stats.stackexchange.com/questions/23993/how-to-correlate-two-time-series-with-possible-time-differences/23995#23995) 

This deals finding the optimal lag, using the spectral coherence. R has functions to compute the power spectral densities, auto and cross correlations, Fourier transforms and coherence. You have to right code to find the optimal lag to obtain the max. weighted coherence. That said, a code for weighting the coherence vector using the spectral density must also be written. Following which you can sum up the weighted elements and average it to get the similarity observed at the optimal lag.
Have you tried another approach for climate signal detection/modelling, like a wavelet analysis? The big problem that can arise with the DFT in climate analysis is actually what you mention: the oscillations are not perfectly periodic and they usually have different time spans so they can actually have many different oscillation ranges, which is pretty confusing from a Fourier Transform perspective. 

A wavelet analysis is more suitable to climate signals because they allow you to check different time spans of oscillation; just as different frequencies are played at different times by a musical instrument, you can check different frequencies in different time spans with the wavelet transform. 

If you are interested, this [paper by Lau & Weng (1995)](http://journals.ametsoc.org/doi/pdf/10.1175/1520-0477%281995%29076%3C2391%3aCSDUWT%3E2.0.CO;2) should erase most of your doubts about this method. The most interesting part is that the wavelet transform of a model versus that of the data are almost directly comparable, because you can directly compare the time span that your model predicts, leaving out all of the spurious oscillation ranges that it doesn't. 

**PS:** I have to add that I wanted to post this as a comment, because it is not actually what the OP's is asking for, but my comment would have been too large and decided to post it as an answer that might come in handy as an alternative approach to that of DFT's.