We are right on the verge of recognizing a resolution tradeoff, not only between and but also with ,the time duration of the data sample. The inequality will be further interpreted and rederived from a somewhat different point of view in the next section. In time-series analysis we have the concept of coherency which is analogous to the concept of correlation defined in Sec. Now if x t and y t are time series, they may have a relationship between them which depends on time-delay, scaling, or even filtering. The generalization of the correlation concept is to define coherency by Correlation is a real scalar.
Coherency is complex and expresses the frequency dependence of correlation.
In forming an estimate of coherency it is always essential to simulate some ensemble averaging. 4-4 Figure 5 Model of random time series generation.