时变连贯性

Fourier-domain coherence is a well-established technique for measuring the linear correlation between two stationary processes as a function of frequency on a scale from 0 to 1. Because wavelets provide local information about data in time and scale (frequency), wavelet-based coherence allows you to measure time-varying correlation as a function of frequency. In other words, a coherence measure suitable for nonstationary processes.

To illustrate this, examine near-infrared spectroscopy (NIRS) data obtained in two human subjects. NIRS measures brain activity by exploiting the different absorption characteristics of oxygenated and deoxygenated hemoglobin. The recording site was the superior frontal cortex for both subjects and the data was sampled at 10 Hz. The data is taken from Cui, Bryant, & Reiss (2012) and was kindly provided by the authors for this example.

In the experiment, the subjects alternatively cooperated and competed on a task. The period of the task was approximately 7.5 seconds.

加载Nirsdata; figure plot(tm,NIRSData(:,1)) hold上情节（TM，Nirsdata（：，2），'r'） 传奇（'Subject 1','Subject 2','地点','NorthWest'）xlabel（'Seconds') title('NIRS Data') grid上; holdoff;

检查时间域数据，尚不清楚单个时间序列中存在哪些振荡，或两个数据集共有哪些振荡。使用小波分析回答两个问题。

Obtain the wavelet coherence as a function of time and frequency. You can use wcoherence to output the wavelet coherence, cross-spectrum, scale-to- frequency, or scale-to-period conversions, as well as the cone of influence. In this example, the helper functionhelperPlotCoherencepackages some useful commands for plotting the outputs ofwcoherence.

[wcoh,~,f,coi] = wcoherence(NIRSData(:,1),NIRSData(:,2),10,'numscales'，16）;helperPlotCoherence(wcoh,tm,f,coi,'Seconds','赫兹');

In the plot, you see a region of strong coherence throughout the data collection period around 1 Hz. This results from the cardiac rhythms of the two subjects. Additionally, you see regions of strong coherence around 0.13 Hz. This represents coherent oscillations in the subjects' brains induced by the task. If it is more natural to view the wavelet coherence in terms of periods rather than frequencies, you can input the sampling interval. With the sampling interval,wcoherenceprovides scale-to-period conversions.

[wcoh,~,P,coi] = wcoherence(NIRSData(:,1),NIRSData(:,2),seconds(1/10),...'numscales'，16）;Helpplotcoherence（WCOH，TM，秒（P），秒（COI），，'Time (secs)','Periods (Seconds)');

同样，请注意与对象在整个录音中发生的心脏活动相对应的相干振荡，大约一秒钟。与任务相关的活动也很明显，大约为8秒。请咨询Cui，Bryant和Reiss（2012），以对此数据进行更详细的小波分析。

In summary, this example showed how to use wavelet coherence to look for time-localized coherent oscillatory behavior in two time series. For nonstationary signals, a measure of coherence that provides simultaneous time and frequency (period) information is often more useful.

Reference: Cui, X., D. M. Bryant, and A. L. Reiss. "NIRS-Based hyperscanning reveals increased interpersonal coherence in superior frontal cortex during cooperation." Neuroimage. Vol. 59, Number 3, 2012, pp. 2430-2437.