绘制周期性时间序列的 FFT 实部与虚部时，对称性意味着什么
正如主题所说，绘制 FFT 的实部与虚部的图形时，对称性意味着什么？聚类是否意味着数据具有周期性？
我问这个问题是因为我做了一个用神经网络预测太阳黑子计数的项目，并且必须找到数据的周期性（并且使用了有效的 FFT）。
有人建议我看看绘制实部与虚部的图表，但我不明白我在看什么。
As the subject says, What does the symmetry mean when graphing real vs imaginary components of a FFT? And does the clustering imply periodicity in the data?
I ask this because I did a project with predicting sunspot count with a neural network and had to find the periodicity of the data (and used FFT which worked).
Someone recommended I look at graphing the real vs imaginary components, but I don't understand what I am looking at.
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任何实值信号的傅里叶变换都将具有埃尔米特对称性，这意味着正值的变换值频率和负频率将是彼此的复共轭。因此，实值是相同的，虚值是彼此的负数，如图所示。
放弃负频率并再次绘制图表可能会更有趣。
对于你的第二个问题，你的结果似乎聚集在 0,0 周围，所以不，聚集并不意味着周期性。变换中的大值意味着相关频率处的周期性。
然而，你有两个大的组成部分，一个主要是真实的，一个主要是虚构的。 “频域中的实数”的另一种思考方式是“像时域中的余弦”，而“频域中的虚数”是“像时域中的正弦”。您的数据集可能并不完全从太阳黑子周期开始，因此该周期看起来像正弦和余弦的组合。如果滑动数据集，实部和虚部的相对幅度可能会发生变化。
我之前曾提出，相位差可能意味着夏季和冬季的活动不同，但这会显示为基频两倍的分量。
The Fourier transform of any real-valued signal will have Hermitian symmetry, meaning the transform values of the positive frequencies and negative frequencies will be complex conjugates of each other. Therefore the real values are the same, and the imaginary values are negatives of each other, as your picture shows.
It would probably be more interesting to drop the negative frequencies and do your graph again.
For your second question, your result appears to be clustered around 0,0, so no, the clustering does not imply periodicity. Large values in the transform imply periodicity, at the related frequency.
However, you have two large components, one primarily real and one primarily imaginary. Another way of thinking of "real in the frequency domain" is "like a cosine in the time domain", while "imaginary in the frequency domain" is "like a sine in the time domain." Your data set probably doesn't start exactly on a sunspot cycle, so the cycle looks like the combination of a sine and cosine. If you slide the data set, the relative amplitudes of the real and imaginary parts will probably change.
I had earlier suggested that the phase difference might imply differing activity in summer and winter, but that would show up as a component at twice the base frequency.