Characterization of signals consisting of multiple time-varying sinusoidal components. Issue 1 (4th January 2016) - Sotelo-Castañon, Julian; Gutierrez-Robles, Jose Alberto; Moreno, Pablo; Galván-Sánchez, Veronica Adriana; García-Sánchez, Jorge Luis; Bañuelos-Cabral, Eduardo Salvador
Abstract : Purpose: – Most systems have a non-linear (NL) behavior and measured signals reflect this non-linearity such that in general they are composed with more than one sinusoidal component. NL analysis methods represent an option for analyzing such signals, however these methods have been developed for single frequency signals, this forces to implement a components separation procedure before performing the signal analysis. The purpose of this paper is to present a new method for analyzing multi-component signals that allows calculating amplitude, frequency and damping constants of the contained sinusoidal components. The method is able to simultaneously identify the different components within a detection bandwidth without previous separation of mono-components, as needed for most methods in used today. Design/methodology/approach: – The method proposed in this work characterizes sinusoidal signals determining their amplitude, frequency and damping constant. This method is based on transforming from the time domain to the z-domain an oscillatory signal that may or may not possess damping. Since frequency and damping of a signal can be determined knowing its z-domain poles, using the signal in z-transform domain an equations system to find the signal poles can be written. Findings: – From the results it can be concluded that the proposed method is reliable and consistent. One quality of the method is its short delay, when the procedure starts there is a delay equal to the time needed to accumulate four samples for each detectable frequency in order to perform the first calculation, after this, the algorithm can deliver a result at each sampling instant. This short delay and the low complexity of the algorithm can permit using the method in real time applications. Originality/value: – The proposed method is able to determine frequencies, damping constants and amplitudes of the components of a signal without a previous separation of mono-components, in contrast with other methods that require filter banks tuned using a previous knowledge of the signal. Moreover unlike techniques such as the Hilbert-Huang Transform the proposed method can be applied to signals with components having very close frequencies.