The primary object of this study is to measure the complexity of different types of signals. We undertake the experiment to support the hypothesis of inverse dispersion entropy (IDE). Multiscale inverse dispersion entropy (MIDE) is also proposed to measure the intrinsic properties of the dynamic system. In addition, this work forms fractional inverse dispersion entropy (FIDE) and \(s^\alpha \) fractional inverse dispersion entropy (SFIDE) inspired in the properties of fractional calculus. Numerical simulations from different categories are applied to test the effectiveness of the proposed methods. Then, we apply the means to heart rate fluctuation data derived from healthy subjects and unhealthy subjects. Experimental results show that dispersion entropy and IDE can make us have a more complete understanding concerning signal complexity. Besides, MIDE method can distinguish the healthy state, pathological state and aging pattern. SFIDE is more sensitive to the change of the fractional order than FIDE.

本研究的主要目的是测量不同类型信号的复杂性。我们进行实验以支持逆色散熵 (IDE) 的假设。还提出了多尺度逆色散熵（MIDE）来测量动态系统的内在特性。此外，这项工作形成分数反色散熵（FIDE）和\(s^\alpha\)分数逆色散熵 (SFIDE) 灵感来自分数阶微积分的特性。应用不同类别的数值模拟来测试所提出方法的有效性。然后，我们将平均值应用于来自健康受试者和不健康受试者的心率波动数据。实验结果表明，色散熵和IDE可以使我们对信号复杂度有更全面的了解。此外，MIDE方法可以区分健康状态、病理状态和衰老模式。SFIDE 对分数阶数的变化比 FIDE 更敏感。