In this paper, having reviewed necessary preliminaries, including sparsity, Tsallis entropy, diversity, preprocessing, fisher information, and Cramer–Rao bound, we analyze the impact of preprocessing a signal on the signal sparsity related to Cramer–Rao lower bound and its main feature, for example, its reconstruction error. The main idea of this paper is to increase the sparsity of a vector, or to decrease its nonzero elements, then to compute the estimation error bound before and after sparsifying the signal. Finally, the claims are validated numerically. We implement Savitzky–Golay filtering on some ECG signals (applying MIT-BIH database of cardiac signals) and then compress them, to illustrate that the sparsity (the reconstruction error) of non-filtered signal was less (more) than that of filtered one. The results can be useful in signal compression and transmission procedures to have fewer recovery errors.

中文翻译：

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通过预处理步骤降低 Cramer-Rao 下界

在本文中，我们回顾了必要的预备知识，包括稀疏性、Tsallis 熵、多样性、预处理、Fisher 信息和 Cramer-Rao 界，我们分析了预处理信号对与 Cramer-Rao 下界相关的信号稀疏性的影响及其主要特征，例如其重构误差。本文的主要思想是增加一个向量的稀疏度，或者减少它的非零元素，然后计算信号稀疏前后的估计误差界。最后，声明在数字上得到验证。我们对一些 ECG 信号（应用 MIT-BIH 心脏信号数据库）实施 Savitzky-Golay 滤波，然后对其进行压缩，以说明未滤波信号的稀疏性（重构误差）小于（大于）滤波信号的稀疏度（重建误差） .