The temporal amplitude envelope of a signal is essential for its complete characterization, being the primary information-carrying medium in spoken voice and telecommunications, for example. Envelope detection techniques have applications in areas like health, sound classification and synthesis, seismology and speech recognition. Nevertheless, a general method to digital envelope detection of signals with rich spectral content doesn't exist, as most methods involve manual intervention, in the form of filter design, smoothing, as well as other specific design choices, based on a priori knowledge about the nature of the specific waves under investigation. To address this problem, we propose a framework that uses intrinsic characteristics of a signal to estimate its envelope, completely eliminating the necessity of parameter tuning. The approach here described draws inspiration from geometric concepts to isolate the frontiers and thus estimate the temporal envelope of an arbitrary signal; to that end, alpha-shapes, concave hulls, and discrete curvature are explored. We also define entities, such as a pulse and frontiers, in the context of an arbitrary digital signal, as a means to reduce dimensionality and the complexity of the proposed algorithm. Specifically, a new measure of discrete curvature is used to obtain the average radius of curvature of a discrete wave, serving as a threshold to identify the wave's frontier points. We find the algorithm accurate in the identification of the frontiers of a wide range of digital sound waves with very diverse characteristics, while localizing each pseudo-cycle of the wave in the time domain. The algorithm also compares favourably with classic envelope detection techniques based on filtering and the Hilbert Transform.

中文翻译：

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通过任意实信号的几何特性进行稳健的数字包络估计

信号的时间幅度包络对其完整表征至关重要，例如，它是语音和电信中的主要信息承载媒介。包络检测技术在健康、声音分类和合成、地震学和语音识别等领域都有应用。然而，并不存在对具有丰富频谱内容的信号进行数字包络检测的通用方法，因为大多数方法都涉及人工干预，形式包括滤波器设计、平滑以及其他特定设计选择，基于关于以下方面的先验知识正在调查的特定波浪的性质。为了解决这个问题，我们提出了一个框架，它使用信号的内在特征来估计其包络，完全消除了参数调整的必要性。这里描述的方法从几何概念中汲取灵感，以隔离边界，从而估计任意信号的时间包络；为此，探索了 alpha 形状、凹包和离散曲率。我们还在任意数字信号的上下文中定义了实体，例如脉冲和边界，作为降低所提出算法的维数和复杂性的一种手段。具体来说，一种新的离散曲率度量用于获得离散波的平均曲率半径，作为识别波前沿点的阈值。我们发现该算法在识别具有非常多样化特征的各种数字声波的前沿方面是准确的，同时在时域中定位了波的每个伪周期。