基于三角样条小波变换和三角样条插值信号重构方法

Signal Reconstruction Method Based on Trigonometric Spline Wavelet Transform and Trigonometric Spline Interpolation

文献8使用二进小波变换提取信号边缘特征,根据信号特征点的值和导数值用三次埃米特多项式进行插值重构。该文分析了文献8存在的两个问题,并针对这两个问题进行改进,即在二进小波变换和插值重构时使用同一种函数———三角样条小波函数,这样才能体现出信号处理的本质。文章作者曾提出的三角样条小波正好同时具有作为小波函数和插值函数双重作用,大大提高信号重构质量。就信噪比和相对误差两项指标与Mallat算法和文献8算法进行了比较,效果明显。

Multiscale edges of a signal can be detected by dyadic wavelet transform.A reconstruction algorithm by cubic spline function interpolation,which is used to recover a signal from its dyadic wavelet transform extrema is proposed in paper ,but two problems exist.They are improved in this paper,i.e.the same function,trigonometric spline function,be used in dyadic wavelet transform and interpolating reconstruction.This can truly express the essence of signal processing.Trigonometric spline wavelet had ever been present by the author of this paper,as a wavelet function,can be used to interpolate.Then advanced the algorithm of the paper.The algorithm of this paper is used to reconstruct six typical signals and compared to algorithms of Mallat's and papers.It shows high signal-noise ratio,low relative errors.