能量有限实序列信号对称性度量

A Measurement for Real Finite Energy Signal Symmetry

为了定量描述滤波器序列的对称程度,同时给滤波器序列提出新的数量特征。对能量有限的实离散时间信号——即实序列在空间域内进行了对称(反对称)性分析。首先提出序列信号一般意义下的对称(反对称)概念,然后由内积空间中的投影、正交分解理论以及内积量化两个信号线性相关程度的特性导出任意信号的对称分解及对称程度序列,对称程度序列定量刻画了信号随对称点的变化时对称特性的变化,在此基础上得出任意序列信号对称程度的定量指标——对称性指标。同时给出了序列信号的对称性定量分析技术。最后对经典和最小不对称Daubech ies低通和高通滤波器系数序列的对称性分别进行了分析,得到了与直观相符的结果,所得到的对称性指标值正好定量地印证了Daubech ies滤波器对称特征。

In order to depict the symmetry degree of filter sequence quantificationally and furthermore propose some new quantitative characters of filter sequence, the symmetry of real discrete-time signals or real sequence in spatial domain was analyzed. Firstly, the generic conception of symmetry for a real sequence was proposed, and then, the symmetry-decomposition and the symmetric degree sequence are presented, which are deduced from the projection theory, the orthogonal-decomposition theory in inner product space and the characteristic of inner product which shows linear similarity degree between signals. The symmetric degree sequence showed that the symmetry of discrete-time real signal changes with the shift of center symmetric point. Based on the symmetric degree sequence, the quantitative symmetric index of a discrete-time real signal was deduced, and the quantificational analysis techniques of symmetry were given. Finally, the symmetry degree of the classical and the least asymmetrical Daubechies of scaling Low-pass Filters sequence and High-pass Filters sequence were analyzed. The results showed that the quantitative analysis is consistent with our intuitionistic instance. These symmetry indexes confirmed the symmetric characters of Daubechies Filters quantificationally.