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本文揭示了一个事实，小波不仅可构成Ｌ２空间中的正交基，小波分解与重构滤波还可产生Ｎ维空间中的正交基．在本文提出修改的小波变换算法之下，Ｎ点信号的小波变换等价于Ｎ维空间中的正交变换．用该算法进行信号或图象压缩，无需对信号或图象进行周期延拓，可严格地在Ｎ维空间中进行．
This paper reveals the fact that wavelet can not only form the orthogonal basis in L2 space, but wavelet decomposition and reconstruction filtering can also generate orthogonal basis in N-dimensional space. Under this modified wavelet transform algorithm, the wavelet transform of N-point signal is equivalent to the orthogonal transform in N-dimensional space. With this algorithm for signal or image compression, no periodic extension of the signal or image can be performed rigorously in N-dimensional space.