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本文把2带的Walter子波抽样定理扩展到M带子波空间,构造出一类M带紧支撑正交插值尺度函数,并在一定范围内将其参数化。举例构造并证明了一个2阶3带插值尺度函数不仅是正交的,而且也是连续的。具有这样性质的Walter抽样定理(1992)在对多分辨空间的信号进行D/A转换时,除了计算机的有限字长误差外,没有任何截断误差。
In this paper, the Walter wavelet sampling theorem of 2-band is extended to the M-band wavelet space to construct a class of orthogonal interpolation scaling function with tight support of M-band and parameterize it within a certain range. An example is constructed and proved that a second-order 3-band interpolation scale function is not only orthogonal but also continuous. The Walter Sampling Theorem (1992), with such properties, does not have any truncation error except for the limited finite length error of a computer when it performs D / A conversion on a signal in a multiresolution space.