Special form test signals formation based on exponential splines
Journal Title: Механіка гіроскопічних систем - Year 2018, Vol 0, Issue 35
Abstract
The usage of special form test signals, indicated as a sum of exponentials, allows the productivity increasing and simplifies the monitoring technique of the complex multi-element electrical circuits parameters. To generate such signals the discrete synthesis technique based on exponential spline models is proposed. Special exponential splines are considered in article. These splines are based on functions that described real transient signals in linear circuits. A definition of such splines is given. Exponential splines can be expressed as a combination of base splines on finite interval. The essence of the method of test signals generating is to represent such signals as a sum of time-shifted finite exponential splines with weight coefficients. The circuit generalized model of signal formation by splines (spline-approximation filter) is analyzed. The model includes a pulse element, a reduced discrete part, and a reduced continuous part. The transfer function equation of the reduced continuous part determines the type of functions producing spline on each sampling interval. Requirements to ensure continuity of the spline function and its derivatives for the transfer function of continuous part are proposed. The choice of transfer function type of the reduced discrete part ensures the finite duration of base functions. It is shown that the base exponential spline is a reaction of such a circuit to a single discrete sample (impulse response characteristic). This approach allows us to synthesize the majority of different exponential splines based on typical models of linear electric circuits. Examples of synthesized splines of the second and third orders are given. The implementation of signal formation method based on exponential splines increases the accuracy of exponential test signals generation with limited number of approximation sections, namely signals that are described by the same functions as splines. This improves the accuracy of the electrical circuits parameters measuring and expands the range.
Authors and Affiliations
Yu. Shumkov, M. Grashenko, V. Daragan
Keywords
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