Teager–Kaiser energy methods for signal and image analysis: A review

Selected Rolling Bearing Fault Diagnostic Methods in Wheel Embedded Permanent Magnet Brushless Direct Current Motors

“…The TKEO filter-Teager-Kaiser energy operator, in its original version was used to process speech and estimate transient signal frequency [31,32]. Another application was in electric machine diagnostics [31,33].…”

“…The basic version of the filter for continuous signals is expressed as dependence (15) and transforms a sinusoidal signal of a given frequency into a constant value. If an input signal is a sum of many signals, then the signal obtained after the transformation depends also on their mutual effect in accordance with (16) and (17) [32]. Hence, the presence of a non-zero constant component in the resultant signal.…”

“…For the purpose of using a TKEO filter in calculations made for a discrete signal, sampled at time interval ∆t, a function derivative must be replaced with its discrete version (18), which will lead to the form compliant with dependence (19). For a constant sampling frequency, the formula can be simplified and ordered to take form (20), which shows the simplicity of the used filtration method: three signal samples are needed, and the additional calculation input is insignificant [31,32].…”

“…In [32] it was shown that the transformation of a signal including numerous frequency components (f 1 , f 2 , f 3 , . .…”

“…Energies 2019, 12 FOR PEER REVIEW 7 In [32] it was shown that the transformation of a signal including numerous frequency components (f1, f2, f3, …) leads to signal () containing components of sums and differences of frequencies f1 ± f2, f1 ± f3, f2 ± f3, … Thus, in the case of faults resulting in amplitude modulation, according to (6) and with consideration for various values of k, m in this dependence, in signal spectrum () frequencies fr, 2·fr, fbf, 2·fbf, etc., should be strengthened. For the purpose of illustrating the characteristic features of the above listed signal processing methods, Figure 1 presents the analysis of a sample amplitude modulated signal.…”