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.
