沃尔什—哈达玛变换(WHT)系数偶数性的理论、应用与实现

本文对文1]提出的一维WHT(A=Hx)系数的奇偶性给出了十分简扼的证明,并提出A系数的奇偶性与sum from j-1 to N Xj的奇偶性相同;二维WHT(A=H_1XH_2)的系数也具有奇偶性、且与sum from νj-1 to N_1·N_2 Xij的奇偶性相同的结论。进而,文章着重导出了量化数据的一维以及二维WHT的系数可全认做偶数的重要结论。文章指出,变换系数的偶数性,仅为WHT所独有,这进一步提高了WHT的数据压缩率,使得WHT成为更加有效可行的数据压缩手段。

PARITY OF THE COEFFICIENTS OF A WHT ——THEORY, APPLICATION AND REALIZATION

This paper gives a very simple and clear proof to the parity of the coefficients of one dimension Walsh—Hadamard Transform ((A)=H(X)) presented by article 1], and points out: the parity of coefficients of A is the same as that of sum from j=1 to N xj; the coefficients of two dimension WHT (A=H_1XH_2) also have the parity and it's the same as the parity of sum from j=1 to N1,N2 Xijo Then, thesis emphatically leads out the coefficients of one dimension or two dimension WHT may be all regarded as a even. The eassy points out the even property of the coefficients of transform is possessed only of by the WHT, and it raises further the rate of data compression of the WHT; as a important means for the data compression, the WHT is more efficient and feasible.