How to analyze sample time series/spectral data?

Good day!

It has 2 data samples (time series), which later built the spectrogram. The first - "TO", followed by a experiment, get the second sample "AFTER". I.e. one sample unit is not a number or specific value, and a sequence of values (and quite large). The volume of sample with 30 to 40 elements (the same BEFORE and AFTER).

Objective: to find an adequate method for the statistical evaluation of the sample. The main hypothesis: are there differences BEFORE and AFTER if Yes, I would like to somehow characterize them.

Clearly, there need a test for dependent samples. If we compared the sets of individual values BEFORE and AFTER the issue would not exist. It seems that the comparison of a long series of 30-40 "head" or very difficult, or ineffective, because it is necessary to compare some sort of "compressed information" of these series. But what to compare? I see 2 options:
1. The selection in the source files "key metrics" for comparison (e.g., frequency and amplitude of the first 3 (5?, 10?) the maximum peaks, indicators of variation, some derived from the entire sequence characteristics etc.). If so, what metric to choose? Next, see this as a 5-10 set of metrics with which to work, for example, by the method of principal component analysis (PCA) and standartnymi tests.
2. The same thing, but for the spectra of the source files. Here, I would pay attention to the frequency and amplitude of the first 3 (5?, 10?) highs. But maybe there's something better (something else)?

If necessary, describe the detailed characteristics of the source sequences.
If there's a suitable or a close decision for Python (library what special) - I will be grateful!
March 20th 20 at 11:44
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