WSEAS Transactions on Signal Processing
Print ISSN: 1790-5052, E-ISSN: 2224-3488
Volume 9, 2013
Adaptive Approach Based on Curve Fitting and Interpolation for Boundary Effects Reduction
Authors: ,
Abstract: Boundary effects are caused by incomplete data in the boundary regions when the analysis window gets closer to the edge of a signal. Various extension schemes have been developed to handle the boundaries of finite length signals to reduce the boundary effects. Zero padding, periodic extension and symmetric extension are some basic extension methods. However, it is well known that all of these solutions may have drawbacks. In this paper, we consider the problem of handling the boundary effects due to improper extension methods in the wavelet transform. An extension algorithm based on curve fitting with properties that make it more suitable for boundary effects reduction is presented here. This extension algorithm could preserve the time-varying characteristics of the signals and be effective to reduce distortions appearing at the boundary. Then, an interpolation approach is used in the boundary effects region to further alleviate the distortions. Procedures for realization of these two algorithms and relative issues are presented. Several experimental tests conducted on synthetic signals exhibiting linear and nonlinear laws are shown that the proposed algorithms are confirmed to be efficient to alleviate the boundary effects in comparison to the existing extension methods.
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Keywords: Finite-length Signals, Convolution, Wavelet Transform, Boundary Effects, Fourier Series Extension, Interpolation