有限区间信号边界效应问题的研究

RESEARCH ON THE EDGE EFFECT OF CUTOFF SIGNAL WITH LIMITED TIME DOMAIN

研究了截断信号边界的“吉布斯”现象及数字滤波器相位特性对有限区间信号滤波处理的影响。在阐明了有限区间信号处理中边界效应物理本质的基础上 ,探讨了数字信号处理中通常所采用的边界处理方法的有效性问题。提出了一种命名为端值延拓法的新的边界处理方法。通过比较分析和实例验证表明这种方法的优越性。文中以零相位数字滤波及运用MALLAT算法对有限区间信号进行小波分解与重构为实例 ,介绍了其边界效应问题及解决方案 ,取得了很好的效果。

The effects of the Jibbs'phenomenon and the phase property of the digital filter on the edges of cutoff signal with limited time domain after filtered is studied.After explaining the physical principle of the edges'effects of the cutoff signal,the effectiveness of the usually used treatment methods for the edges is discussed and a new treatment means named edgevalue_padding expansion is put forward.Testifying and comparing with other classical treatment means such as zero_padding expansion,symmetry_padding expansion,smooth_padding expansion etc.exibit fully its advantages.Examples of zero_phase distortion filter and decomposition and reconstruction of the limited fine domain signals by discrete wavelet transform using Mallat algorithm are given to testify the strong points of edge_value_padding expansion.