Application of the Savitzky-Golay differentiating filter in restoring the sensor input signal

The problem of correcting the dynamic error by restoring the sensor input signal in the presence of additive noise at its output is considered. A review of publications on the application of the Savitzky-Golay fi lter in dynamic measurements is carried out. A block diagram of an adaptive dynamic measuring system based on the discrete Savitzky-Golay differentiating fi lter is developed. For the possibility of using the differentiating fi lter, a method is proposed for reducing the sensor transfer function to a minimum form of an integrating unit, the order of which is equal to the difference in the orders of the denominator and numerator of the sensor transfer function. Reduction is performed by processing a sequence of discrete samples of the sensor output signal using a reduction unit, the output signal of which is equivalent to the output signal of the reduced sensor transfer function. After analyzing the dynamic error of the sensor input signal restoration, an estimate of the error and its components is proposed, due to the difference between the sensor's transfer function and the ideal one and the additive noise at its output. The noise adaptation of the differentiating fi lter parameter is carried out by minimizing the mean square deviation of the dynamic error estimate. A computer simulation of the proposed measuring system is performed in the presence of additive random noise at the output of a second-order sensor. The effectiveness of estimating the dynamic error of reconstructing the sensor input signal based on the structure of a measuring system with the Savitzky-Golay differentiating fi lter is demonstrated. The application fi eld of the measuring system obtained is the measurement data processing of fast-changing quantities such as temperature, pressure, speed and acceleration, when the dynamic component of the error, caused by inertia of the sensor, as well as additive noises at its output, is dominant.

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