Van Baren, P., "An Exploration of Power Spectral Density (PSD) Estimation, with an Introduction to iDOF™ Instant Degrees of Freedom," SAE Technical Paper 2015-01-2620, 2015, doi:10.4271/2015-01-2620.
Random vibration control systems produce a PSD plot by averaging FFTs. Modern controllers can set the degrees of freedom (DOF), which is a measure of the amount of averaging to use to estimate the PSD. The PSD is a way to present a random signal-which by nature “bounces” about the mean, at times making high excursions from the mean-in a format that makes it easy to determine the validity of a test. This process takes time as many frames of data are collected in order to generate the PSD estimate and a test can appear to be out of tolerance until the controller has enough data to estimate the PSD with a sufficient level of confidence. Something is awry with a PSD estimate that achieves total in-tolerance immediately after the test begins or immediately after a change in level, and this can hide dangerous over or under test conditions within specific frequency bands, and should be avoided. This paper intends to treat various methods of dealing with level change, the proper method of dealing with level changes, as well as a PSD estimation method that accurately and quickly estimates the true signal PSD significantly faster than the traditional averaging method: iDOF™.