Hearing aids use dynamic range compression (DRC), a form of automatic gain control, to make quiet sounds louder and loud sounds quieter. Compression can improve listening comfort, but it can also cause unwanted distortion in noisy environments. It has been widely reported that DRC performs poorly in noise, but there has been little mathematical analysis of these noise-induced distortion effects. This work introduces a mathematical model to study the behavior of DRC in noise. By making simplifying assumptions about the signal envelopes, we define an effective compression function that models the compression applied to one signal in the presence of another. Using the properties of concave functions, we prove results about DRC that have been previously observed experimentally: that the effective compression applied to each sound in a mixture is weaker than it would have been for the signal alone; that uncorrelated signal envelopes become negatively correlated when compressed as a mixture; and that compression can reduce the long-term signal-to-noise ratio in certain conditions. These theoretical results are supported by software experiments using recorded speech signals.

中文翻译：

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模拟动态范围压缩对噪声中信号的影响

助听器使用动态范围压缩 (DRC)，一种自动增益控制的形式，让安静的声音变得更响亮，让响亮的声音变得更安静。压缩可以提高聆听舒适度，但它也会在嘈杂的环境中导致不必要的失真。据广泛报道，DRC 在噪声方面表现不佳，但几乎没有对这些噪声引起的失真影响进行数学分析。这项工作引入了一个数学模型来研究 DRC 在噪声中的行为。通过对信号包络进行简化假设，我们定义了一个有效的压缩函数，该函数对在存在另一个信号时应用于一个信号的压缩进行建模。利用凹函数的性质，我们证明了先前通过实验观察到的关于 DRC 的结果：应用于混合中每个声音的有效压缩比单独用于信号时要弱；当作为混合压缩时，不相关的信号包络变得负相关；在某些情况下，这种压缩会降低长期信噪比。这些理论结果得到了使用记录语音信号的软件实验的支持。