Cyclic Averaging for Frequency Response Function Estimation

Cyclic averaging, as a method for reducing the leakage ermr in the estimatian of frequency response functions, is a simple and effective method that can be implemented in any data acquisit ion system. With the widespread availability of multikbamel data acqtisition systems, cyclic averaging may be the easiest approach to minimizing the huncation effect, known as leakage, that DccllIs when time domain data is transformed to the frequency domain utilizing fast Fourier transforms. Cyclic averaging, historically, has been used in rotating equipment data analysis to enhance charactetitics in the data that are functions of the mtating speed. This same data averaging technique can be used when estimating frequency response timctims to enhance the frequency charactedstics in the data that are integer functions of the observation window. In this way, the nonperiodic cbamcteristics in the data are rkdmkd and leakage is reduced. A presentation of the theory of cyclic averaging and its application and effectiveness in a typical freequency response function edmation pmcedue is included. The averaging of signals is normally viewed as a summation 01 weighted summation process where each sample function has a common abscissa. Normally, the designation of hirrory is given ta sample functions with the abscissa of absolute time and the designation of speclm is given to sample functions with the abscissa of absolute frequency. Tbe spectra are normally generated by Fourier transforming the corresponding history. In order to generalize and consol idate the concept of s ignal averaging as much as poss ible , the case of relative time can also be considered. In this way relrrfive history can be discussed with units of the appmpriate event rather than seconds and a relative spccbum will be the corresponding Fourier transform with units of cycles per event. Axis concept of signal averaging is used widely in stmctuml signature analysis where the event is a revolutioo. This kind of approach simpliks the application of many other concepts of signal relationships such as Shannon’s sampling theorem and Rayleigh’s criterion of frequency resolution.