Sliding Discrete Linear Canonical Transform
Sliding Discrete Linear Canonical Transform
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DOI：
10.1109/tsp.2018.2855658
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发表时间：
2018-09
影响因子：
5.4
通讯作者：
Yannan Sun;Bingzhao Li
中科院分区：
文献类型：
--
作者：
Yannan Sun;Bingzhao Li
线性正则变换（LCT）已被证明是信号处理中最强大的工具之一，在本文中，我们提出了一种计算离散LCT（DLCT）的自适应方法，称为滑动离散线性正则变换（SDLCT）。首先，我们介绍了一种单点DLCT方案，它可以有效地计算单个或几个线性正则谱。其次，SDLCT提出了基于迭代算法，以满足在线谱分析的要求时，只有一个子集的$N$频率需要从$\tilde{N}\hbox{--}$点离散LCT（$N\leq \tilde{N}$）。文中还详细讨论了算法的可加性和可逆性。第三，通过DLCT卷积运算减少了算法的频谱泄漏，并通过频域卷积实现了时域加窗。最后，我们提出了两种方法来评估性能方面的计算复杂度和精度，并显示所得出的结果的正确性。
The linear canonical transform (LCT) has been shown to be one of the most powerful tools in signal processing, and in this paper, we propose an adaptive approach for the computation of the discrete LCT (DLCT), termed the sliding discrete linear canonical transform (SDLCT). First, we introduce a scheme for the single-point DLCT, which can effectively calculate a single or a few linear canonical spectra. Second, the SDLCT is proposed based on an iterative algorithm to meet the requirements of online spectral analysis when only a subset of $N$ frequencies are required from an $\tilde{N}\hbox{--}$point discrete LCT ( $N\leq \tilde{N}$). The additivity and reversibility properties of the proposed algorithms are also discussed in detail. Third, the DLCT convolution operation is obtained to reduce the spectral leakage of the proposed algorithm, and time-domain windowing is implemented via frequency-domain convolution. Finally, we present two methods to assess performance with regard to computational complexity and precision and to show the correctness of the derived results.