Aiming at the fact that traditional signal reconstruction method based on traditional methods such as Fourier and wavelets transformations cannot preserve the sharp features in the original data well, a signal reconstruction method is proposed in this paper based on a class of orthogonal piecewise polynomial function system—named as V-system. Firstly, different types of feature points of the original data are obtained through the feature extraction algorithm; secondly, the feature points are reparametrized to the locations of different knots in the V-system; finally, the fitted signal is obtained by solving the least-squares linear equations with constrains. Because the V-system has basis functions with different smoothness, the reconstructed signal can capture different features in the original data. Numerical experimental results show that the proposed method in this paper not only obtains a reconstructed signal reflecting the global shape of the original data, but also can accurately reproduce sharp features.
To address the fact that the traditional curve fitting method based on B-spline basis functions cannot preserve the sharp features in the original data well, a curve fitting method based on a class of orthogonal piecewise polynomial function Vsystem is proposed in this research. Firstly, different types of feature points from the original data are extracted by using the feature extraction algorithm; secondly, the feature points are reparametrized to the locations of different knots in the V-system; finally, the fitting curve is obtained by solving least-squares linear equations with constraints. Different features in the original data can be captured since the V-system contains basis functions with different smoothness. Numerical experimental results show that the proposed method in this research creates a fitted curve reflecting the global shape of the original data and can accurately represent sharp features.
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