At a given instant, point `a' moves up while point `b' moves down. After a time interval these directions are reversed. Hence is a measure of a time period of fluctuation of an eddy of size of and is the associated frequency. A distribution of eddy sizes now means that there exists a distribution of frequencies as well. In a boundary-layer, where is the boundary-layer thickness and the largest value of the time period can be estimated conservatively as . In flow past a cylinder may be chosen as the cylinder diameter; in flow past a mesh the grid size or the wire diameter whichever is larger can be used as an estimate of . As a rule of thumb the integration time should be 5 to 10 times the characteristic time period .

Other quantities that are frequently required in the study of stationary random signals with a zero mean value are the autocorrelation and power spectrum. These are defined below.

Autocorrelation:

Power spectrum: : is the fraction of the kinetic energy present in the frequency interval .

The largest value of occurs when . For larger values of is only partly correlated with itself and in general as , . Signals for which finite and non-zero are said to be coherent since two widely separated events on the time scale continue to bear a relationship to each other. The quantity

is called the integral time scale and is a measure of the time period over which the signal is correlated with itself. The total time for which the signal is acquired should be larger than , so that the statistics are meaningfully evaluated.