Classical sampling theorems in the context of multirate and polyphase digital filter bank structures
Classical sampling theorems in the context of multirate and polyphase digital filter bank structures
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DOI：
10.1109/29.90376
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发表时间：
1988-09
期刊：
影响因子：
--
通讯作者：
P. Vaidyanathan;V. Liu
中科院分区：
文献类型：
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作者：
P. Vaidyanathan;V. Liu
从所谓的广义样本中恢复信号是一个设计适当的线性滤波器（称为重建（或合成）滤波器）的问题。这种关系进行审查和探讨。新的定理的子采样序列推导出直接使用的数字滤波器组的框架。这些结果与最大抽取数字滤波器组系统的完全重构理论有关。其中一个定理涉及序列的二次采样及其最初的几个差，以及随后以有限代价无错误地稳定重建。重建滤波器原来是无乘法器和FIR（有限脉冲响应）类型。这些想法被扩展到二维信号的情况下，通过使用克罗内克形式主义。还考虑了带限序列的子采样。序列x（n）的傅里叶变换为零mod ω mod >或=L π/M，其中L和M是整数，L >
The recovery of a signal from so-called generalized samples is a problem of designing appropriate linear filters called reconstruction (or synthesis) filters. This relationship is reviewed and explored. Novel theorems for the subsampling of sequences are derived by direct use of the digital-filter-bank framework. These results are related to the theory of perfect reconstruction in maximally decimated digital-filter-bank systems. One of the theorems pertains to the subsampling of a sequence and its first few differences and its subsequent stable reconstruction at finite cost with no error. The reconstruction filters turn out to be multiplierless and of the FIR (finite impulse response) type. These ideas are extended to the case of two-dimensional signals by use of a Kronecker formalism. The subsampling of bandlimited sequences is also considered. A sequence x(n) with a Fourier transform vanishes for mod omega mod >or=L pi /M, where L and M are integers with L >