An Approximate Method for Recovering Input Signals of Measurement Transducers

We consider the problems of information-measuring equipment, modeled by ordinary differential equations, when some physical variable cannot be measured, but its value can be determined by the functional (or operator) of another physical variable available for measurement. Direct application of models with ordinary differential equations for recovering input signals of measurement transducers has not received due development because of the need to calculate (possible high order) derivatives of noisy signals. A method for recovering input signals is proposed, in which the apparatus of hypersingular integrals is used for the approximate calculation of derivatives. We propose approximate methods for calculating derivatives expressed by quadrature formulas for hypersingular integrals. The input signal recovery method has been tested for one accelerometer model. We demonstrate the high effectiveness of the proposed method.