M带Walter子波抽样定理

M-BAND WALTER WAVELET SAMPLING THEOREM

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。

This paper constructs a family of M-band orthogonal compactly supported interpolating scaling function, gives a 3-band scaling function and shows that it is not only compactly supported, but also orthogonal and continuous. G.Walter's wavelet sampling theorem(1992) corresponding to the scaling function has the compactly supported interplant. Therefore, the signals in multiresolution subspaces can be reconstructed exactly and quickly without any truncated errors except finite field length errors.