Continuous piecewise linear approximation based on Haar scale transform
Xingye Li · Journal of Liaoning Technical University · 2010
In order to achieve continuous approximation on nonlinear systems,this paper presents an algorithm for continuous piecewise linear approximation based on Haar wavelet transform.The scaling coefficients are obtained using the Haar scaling transformation of a nonlinear function,and then the continuous piecewise linear approximation of the nonlinear function is reconstructed using the compactly supported continuous piecewise linear basis functions.Theoretical analysis proves that the approximation can achieve any accuracy.The simulation demonstrates that the error convergence of the continuous piecewise linear approximation is more uniform than that of the Haar wavelet approximation.It is an obvious advantage that the algorithm provides an analytical expression of approximation.Since the computational complexity of the Haar scale transform(correspond to arithmetic average) is low and the structure of the compactly supported continuous piecewise linear basis functions is simple,it is ease for a wide application of proposed algorithm.