The Theory of Multiresolution Analysis Frames and Applications to Filter Banks
The Theory of Multiresolution Analysis Frames and Applications to Filter Banks
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DOI：
10.1006/acha.1997.0237
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发表时间：
1998-10
影响因子：
2.5
通讯作者：
J. Benedetto;Shidong Li
中科院分区：
文献类型：
--
作者：
J. Benedetto;Shidong Li
摘要提出了帧多分辨率分析的概念。FMRA是多分辨率分析（MRA）的经典概念的仿射框架的自然扩展。FMRA的相关理论比MRA复杂。该理论的一个基本结果是用函数φ的傅里叶变换的可计算周期的不连续性和零集来刻画函数φ的整数平移的框架。存在与每个FMRA相关联的子带编码滤波器组。在数学上，这些滤波器组可以用于为有限能量信号构造新的帧。与MRA一样，FMRA滤波器组在定义FMRA的逐次逼近子空间中的任何一个中提供所有有限能量信号的完美重构。与MRA相比，与FMRA相关联的完美重构滤波器组可以是窄带的。由于这个特性，在信号处理中，FMRA滤波器组在重建给定窄带信号的同时实现量化噪声降低。
Abstract The notion of a frame multiresolution analysis (FMRA) is formulated. An FMRA is a natural extension to affine frames of the classical notion of a multiresolution analysis (MRA). The associated theory of FMRAs is more complex than that of MRAs. A basic result of the theory is a characterization of frames of integer translates of a function φ in terms of the discontinuities and zero sets of a computable periodization of the Fourier transform of φ. There are subband coding filter banks associated with each FMRA. Mathematically, these filter banks can be used to construct new frames for finite energy signals. As with MRAs, the FMRA filter banks provide perfect reconstruction of all finite energy signals in any one of the successive approximation subspaces V j defining the FMRA. In contrast with MRAs, the perfect reconstruction filter bank associated with an FMRA can be narrow band. Because of this feature, in signal processing FMRA filter banks achieve quantization noise reduction simultaneously with reconstruction of a given narrow-band signal.