In information and measuring technology, there are a large number of tasks when some physical variable, the values of which must be determined, are inaccessible to measurements, but its value can be determined knowing the functional (or operator) of another physical variable available to measurements. This range of tasks includes measuring transformers, the dynamics of which is modeled by ordinary differential equations. The direct application of these models for the reconstruction of input signals has not received proper development due to the need to calculate the derivatives (possibly high orders) of signals noisy with interference. In this paper, we propose a method for recovering the input signals of measuring transformers, in which the signal of interest to the observer is associated with the measured signal by the differentiation operator. For the numerical calculation of derivatives, the apparatus of hypersingular integrals is used. Approximate methods for calculating derivatives, expressed by quadrature formulas for hypersingular integrals, are presented. The method for recovering input signals is tested for one accelerometer model. The high efficiency of the proposed method has been demonstrated.