Discretization Accuracy of Continuous Signal Peak Values in Limited Bandwidth Systems

Abstract

In many real or physically modelled processes, it is required to determine the peak values of the signals. Reduced scale measurements in the laboratory must be transformed to a real scale and the maximum errors must be calculated with high accuracy to know and evaluate their impact on the real work. The sampling rate contributes significantly to measurement accuracy and its effect is relevant. Often, the measurement error due to the sampling frequency is not quantified and therefore, measurement specifications are incompletely given. There are not understandable formulations which can be applied to obtain the possible highest errors due to the discretization of the continuous signals, especially when the system bandwidth is limited. In this paper, a wide general analysis is developed based on the relation between the sampling frequency and the maximum measurement error for a sinusoidal signal. The relative maximum errors around the peak values are calculated and their mathematical expressions are obtained; the relative maximum error during the calculation of peak values in post-processing mode is analyzed with more relevance. Additionally, analysis for signals composited of several harmonics is presented. Examples of biomechanical signals and wave research laboratories are analyzed. These errors are quantified in a material very understandable. The cubic spline interpolation is evaluated and its effect is computed. A comparison with works related is detailed.