Piecewise linear approximation of a highly noisy signal waveform using least squares method

Abstract

The rising trend of computer technology using makes digital signal processing (DSP) techniques converted into numerical data sets particularly relevant. For the most part, they are quite complex and their use is not always justified for a wide range of applications. This determines the ongoing interest in heuristic algorithms that are based on simplified approaches and allow quickly obtaining approximation of estimates with the least work amount. This paper discusses a method of pulsed (single) aperiodic signal with a high level of noise component mathematical processing by approximating its shape by a piecewise linear function, that parameters are determined using the method of least squares. A brief justification for this method is given, based on an analysis of the stochastic nature of the noise component. A numerical analysis of the signals spectral composition before and after processing is performed, as well as a comparison with other common methods: filtering and coherent averaging. It is shown that the waveform piecewise linear approximation can effectively separate the useful signal from the noise component, does not require complex algorithmic designs, and its program code implementation is possible in any high-level languages. The developed method is applicable for all types of signals and is most effective for processing single aperiodic pulses without its repetition possibility. The proposed approach can also be used in the educational process when studying the programming basics and for solving economic problems based on the determination of trend lines by parametric methods.