摘要
标准的小波分析方法中,信号的低频能量和高频能量不能人为控制,因此在利用低频分量近似原信号时,在一些陡峭变化区域会存在较大偏差。针对这一问题,本文首先分析了小波分解各子带能量与采样频率的关系,发现增加采样频率可以降低高频能量,并给出了部分证明。以此为基础,提出了非均匀采样信号小波分析误差控制方法,考虑到小波分解的高频能量和低频能量存在互补关系,算法利用高频系数作为低频表示误差的判断指标,对误差超限位置处的数据增如采样,然后对修正后的数据进行低频分解;该方法使低频能量可根据误差门限人为进行调整。重构是分解的逆过程,可完全无误的恢复原始信号。实验表明算法对小波分析低频表示误差具有很好的控制能力。
In the standard wavelet analysis methods（SWAM）,the energy distributed in low band and high band can not be controlled.Large distortion may be produced in some steep changed local region when using low band to approximate the original signal.To solve this problem,the relation between energy distribution in each band and sampbng frequency is analyzed first.It is found that the high-band components＇ energy can be decreased by increasing sampling frequency.And the partial proof is given.Based on this idea,a wavelet analysis method with error control（WAMEC） is presented for non-uniform sampling signal.Taking into account the complementary relation of energy distributed in low-band and high-band,the algorithm uses high-band coefficients as indicator of low-band reconstruction error.The up-sampling is preceded at these positions in which the error exceeds the threshold.At last,low-band components are calculated using modified data.The energy in low-band components can be adjusted by error threshold.The reconstruction is the inversion procedure of decomposition and the original signal can be recovered lossless.The experimental results show WAMEC has well ability to control local error for low-band reconstruction.
出处
《信号处理》
CSCD
北大核心
2012年第1期118-123,共6页
Journal of Signal Processing
基金
国防预研基金
关键词
小波分析
误差控制
非均匀采样
wavelet analysis
error control
non-uniform sampling
