Energy density for signals maximizing the integral-square error. (August 2016) - Tomczyk, Krzysztof; Layer, Edward
Highlights: The review of literature concerning the signals maximizing the integral-square error is presented. The theoretical principles of applied CTW analysis is discussed. The results of mathematical modelling of the accelerometers and maximizing signals are presented. The scalograms and the graphs, illustrating normalised amplitudes vs. frequency for the maximizing signals are shown. The numerical calculations were executed in the MatLab program. Abstract: The paper presents an application of the continuous wavelet transform (CWT) to analyse the energy density of signals which maximize the integral-square error (ISE) at the output of two different accelerometers. These accelerometers were chosen as being examples of a large class of measuring instrument intended for the measurement of nondetermined input signals. Input signals constrained in magnitude only and simultaneously in magnitude and rate of change are considered in this paper. Scalogram analysis which provides a graphical representation of the signal energy density over the time-scale plane is discussed in detail in the second section of this paper. In the third, the results for the two accelerometers modelling are presented, while the fourth section presents methods for determining signals maximizing the ISE by using the genetic algorithm (GA). The final sections is devoted to a discussion of the results and analysis of the energy density based on the scalogram and corresponding conclusions with respect to properly determined signals maximizing ISE. For modelling the sensors MathCad15 was applied, while the maximizing signals and CWT analysis were executed using MATLAB2011. The methods presented in this paper constitute a novel approach for the estimation of the correctness of the signals maximizing the ISE by means of energy density analysis.