如何找到数据的周期性？
我有一个数据集（一个数组），我需要找到其中的周期性。我应该如何进行？有人说我可以使用 FFT，但我不确定它如何给我周期性。感谢您的帮助！
I have a dataset (an array) and I need to find the periodicity in it. How should I proceed? Somebody said I can use FFT but I am not sure how will it give me the periodicity. Your help is appreciated!
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对于此任务，最好使用自相关。
FFT 是用于查找周期性的错误工具。
例如，考虑这样一种情况：波形是通过将两个简单的正弦波相加而成的，一个周期为 2 秒 (0.5 Hz)，另一个周期为 3 秒 (0.333 Hz)。该波形的周期为 6 秒（即 2*3），但傅里叶频谱仅在 0.5 Hz 和 0.333 Hz 处显示两个峰值。
For this task it's best to use the autocorrelation.
The FFT is the wrong tool to use for finding the periodicity.
Consider, for example, a case where your waveform is made by adding together two simple sine waves, one with a period of 2 seconds (0.5 Hz), and the other with 3 seconds (0.333 Hz). This waveform will have a periodicity of 6 seconds (i.e., 2*3), but the Fourier spectrum will only show two peaks at .5 Hz, and .333 Hz.
周期性是一个没有明确定义的术语。例如，这样的数据：
1, 10, 1, 10, 1, 11, 1, 10, 1, 10, 1, 11, 1, 10, 1, 10, 1, 11
您可以将其视为一个不精确但强周期性为 2，精确周期性为 6。
对于精确周期性，您可以简单地尝试将给定数据查找为重复两次的数据子串。
对于真实、噪声信号的非精确周期性，可以使用时域和频域方法。
时域一是自相关。就像上面的子串搜索：搜索数据具有最大自相似性的移位值。
对于简单信号，计算阈值转换可能就足够了。
频域方法包括使用 FFT/FHT 的方法：搜索频率频谱中的最大值，从而给出 1/T 的周期性。
另一种方法是使用倒谱。
Periodicity is not well defined term. For example, such data:
1, 10, 1, 10, 1, 11, 1, 10, 1, 10, 1, 11, 1, 10, 1, 10, 1, 11
you may treat as one with not exact but strong periodicity of 2, and as exact periodicity of 6.
For exact periodicity you may simply try to find given data as substring of data repeated twice.
For non exact periodicity of real, noisy signal time domain and frequency domain methods may be used.
Time domain one is self correlation. It is like a substring search above: searched for a shift value on which data have maximum self similarity.
For simple signals counting threshold transitions may be enough.
Frequecy domain methods include one using FFT/FHT: search for a maximum in fequency spectre which gives 1/T of periodicity.
Another method is using Cepstrum.
这篇新论文并没有引起太多关注，谱聚类
在 oscillat.iab.keio.ac.jp。我不隶属于作者，但将代码放在 GitHub 此处 以便于访问（主脚本此处）。
使用 DFT 并将行分组为主要的光谱功率，根据我的经验，很好用。显然，对于基因组学来说，它的设计是稳健的（在代码中指出，它在计算上是重），因此可能取决于应用程序。
This new paper hasn't had a great deal of attention, spectral clustering
Implemented in an R package available at oscillat.iab.keio.ac.jp. I'm not affiliated with the authors, but put the code up at GitHub here for easier access (main script here).
Uses a DFT and groups rows into major spectral powers, nice to use in my experience. Obviously for genomics it's designed to be robust (noted in the code it's computationally heavy), so may depend on the application.
您可以使用 FFT，因为它将您的数据集从值空间转换为频率空间。
这意味着您最终将拥有一组频率，这些频率组成将产生您想要分析的初始输入。然后您可以轻松识别哪些是由特定频率产生的主要贡献，因此您将了解有多少个周期性以及哪些是最有影响力的。.
看看这里：http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/dft/
You could use FFT because it will convert your data set from a value-space to a frequency-space.
This means that you will end up having a set of frequencies that composed will produce the initial input that you want to analyze. Then you can easily recognize which are the major contribuitions that are generated by specific frequencies and so you will understand how many periodicities there are and which are the most influential ones..
take a look here: http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/dft/
我发现一篇论文将基于 FFT 的周期图与自相关相结合，以提供有关信号周期性的更准确信息。我认为这种方法值得研究：
关于周期性检测和结构周期性相似性< /a>
I found a paper that combines an FFT-based periodogram with autocorrelation to provide more accurate information on the periodicity of a signal. I think that this method could be worth looking into:
On Periodicity Detection and Structural Periodic Similarity