Boundary Effects Reduction in Wavelet Transform for Time-frequency Analysis

Boundary effects are very common in the processing of finite-length signals. In this paper, we consider the problem of handling the boundary effects that can occur due to improper extension methods. Contrary to traditional methods including zero padding, periodic extension and symmetric extension, we propose an extension algorithm based on Fourier series with properties that make it more suitable for boundary effects reduction in the application of time-frequency signal analysis. This extension algorithm could preserve the time-varying characteristics of the signals and be effective to reduce artificial singularities appearing at the boundary. Procedures for realization of the proposed algorithm and relative issues are presented. Accurate expressions for the extent of boundary effects region are derived and show that the extent of boundary effects region is not equivalent to the width of wavelet under current mean square definition. Then, an interpolation approach is used in the boundary effects region to further alleviate the distortions. 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. Key-Words: Finite-length Signals, Convolution, Wavelet Transform, Boundary Effects, Fourier Series Extension, Interpolation