The Double Density DWT
The Double Density DWT
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DOI：
10.1007/978-94-015-9715-9_2
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发表时间：
2001
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影响因子：
--
通讯作者：
I. Selesnick
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文献类型：
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作者：
I. Selesnick
本章讨论了基于过采样滤波器组的离散小波变换的设计。在这种情况下，小波形成过完备基或框架。特别是，我们认为系统的设计是类似于Daubechies的正交小波，也就是说，满足某些多项式性质的最小长度小波滤波器的设计，但现在在过采样的情况下。小波构造使用最大平坦FIR滤波器结合扩展的方法paraunitary矩阵。由于在设计问题中有更多的自由度，本章中描述的小波比相同支撑的正交小波光滑得多。本章所讨论的过采样二进小波变换基于一个尺度函数和两个不同的小波。具有比所需更多的子波使得相同尺度内的相邻子波之间的间隔更近。像双树DWT一样，过采样DWT存在。这里的艾德是冗余因子2，与级别的数量无关。相比之下，非抽取小波变换的冗余度随着层数的增加而增加。
This chapter takes up the design of discrete wavelet transforms based on oversampled filter banks. In this case the wavelets form an overcomplete basis, or frame. In particular, we consider the design of systems that are analogous to Daubechies' orthonormal wavelets-that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. The wavelets are constructed using maximally flat FIR filters in conjunction with extension methods for paraunitary matrices. Because there are more degrees of freedom in the design problem, the wavelets described in this chapter are much smoother than orthonormal wavelets of the same support. The oversampled dyadic DWT considered in this chapter is based on a single scaling function and two distinct wavelets. Having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale. Like the dual-tree DWT, the oversampled DWT present. ed here is redundant by a factor of 2, independent of the number of levels. In comparison, the redundancy of the undecimated DWT grows with the number of levels.