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首页> 外文期刊>IEEE Transactions on Circuits and Systems. I, Regular Papers >Comparative Analysis of Shift Variance and Cyclostationarity in Multirate Filter Banks
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Comparative Analysis of Shift Variance and Cyclostationarity in Multirate Filter Banks

机译：多速率滤波器组中位移方差和循环平稳性的比较分析

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摘要

Multirate filter banks introduce periodic time-varying phenomena into their subband signals. The nature of these effects depends on whether the signals are regarded as deterministic or as random signals. We analyze the behavior of deterministic and wide-sense stationary (WSS) random signals in multirate filter banks in a comparative manner. While aliasing in the decimation stage causes subband energy spectra of deterministic signals to become shift-variant, imaging in the interpolation stage causes WSS random signals to become WS cyclostationary (WSCS). We provide criteria to quantify both shift variance and cyclic nonstationarity. For shift variance, these criteria separately assess the shift dependence of energy and of energy spectra. Similarly for nonstationarity, they separately assess the nonstationary behavior of signal power and of power spectra. We show that, under aliasing cancellation and perfect reconstruction constraints of paraunitary and biorthogonal filter banks, these criteria evaluate the behavior of deterministic and WSS random signals in a consistent, dual way. We apply our criteria to paraunitary and biorthogonal filter banks as well as to orthogonal block transforms, and show that, for critical signals such as lines or edges in image data, the biorthogonal 9/7 filters perform best among these
机译：多速率滤波器组将周期性的时变现象引入其子带信号。这些影响的性质取决于信号是确定性信号还是随机信号。我们以比较的方式分析了多速率滤波器组中确定性和广义平稳（WSS）随机信号的行为。抽选阶段的混叠使确定性信号的子带能谱变得变化，而插值阶段的成像使WSS随机信号变为WS循环平稳（WSCS）。我们提供了标准来量化移位方差和周期性非平稳性。对于位移方差，这些标准分别评估能量和能谱的位移依赖性。类似地，对于非平稳性，它们分别评估信号功率和功率谱的非平稳性。我们表明，在混叠抵消和超unit变和双正交滤波器组的完美重构约束下，这些标准以一致，双重的方式评估确定性和WSS随机信号的行为。我们将标准应用于准unit正和双正交滤波器组以及正交块变换，并表明，对于关键信号（例如图像数据中的线条或边缘），双正交9/7滤波器在这些信号中表现最佳

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