M型正交小波包的构造及在频域内的紧支撑

Construction of Orthogonal M-Wavelet Packet and Properties of Compactly Support

基于多尺度分析理论 ( MRA)与 A.W.W方法构造了 M型小波包 ,并研究其性质 ,如频谱有限性、双尺度序列 (滤波器 ) hn=φ( n/2 )及当 n→∞ ,hn=O( n-N ) .它在小波包应用的计算中速度可比 Shannon小波包快 .另外 ,着重给出了当 l=2 k-1,k∈ Z+ 时 ,{μ2 l( ω) },{μ2 l+ 1( ω) }的紧支撑区间的通式 。

The band limited wavelet can be used to express the local exact character of the signal in frequency. This paper constructed M wavelet by utilizing the Multi Resolution Analysis (MRA) and A.W.W method. A corresponding wavelet packet { μ n(x) } was constructed. Many good properties are proved, e.g., band limited,bi scale sequence (filter) h n=φ(n/2). As n→∞,h n=O(n -N ). So the speed with M wavelet is faster than with Shannon wavelet in computing. At the same time, the compactly supported intervals of ｛ 2l (ω)｝,{ 2l+1 (ω)} are studied when l is 2 k-1 ,k∈Z +.