De Cesaris Simona, D'Orazio Dario, Morandi Federica, Garai Massimo
Department of Industrial Engineering, University of Bologna, Bologna, Italy.
J Acoust Soc Am. 2015 Oct;138(4):2513-23. doi: 10.1121/1.4931904.
The Schroeder's backward integration method and its applications have been widely studied in the literature; some papers analyze the performance of the method, some others suggest various enhancement techniques. In spite of these findings, there exist several cases where the energy decay curve extracted using the classical backward integration method and the parameters computed from it seem not always representative of the phenomenon under study. Among them, the cases where the early decay is dependent on strong, distinct reflections occurring just after the direct wave, as in most Italian opera houses. Other cases are measured impulse responses with a very low signal-to-noise ratio or missing the direct wave. In the literature, alternatives to the Schroeder's method have been proposed, ranging from Hilbert transform to non-linear processing techniques. In this work a method for the extraction of the envelope based on pre-processed energy detection for early decay estimation is proposed. It is shown that it returns an envelope well matching the first part of the decay even in non-linear cases, returning detailed information on the first part of the decay. The performance of the proposed method is presented and discussed for some exemplary impulse responses measured in historical opera houses. A preliminary study on the perceptive relevance of the method is finally presented.
施罗德反向积分法及其应用在文献中已得到广泛研究；一些论文分析了该方法的性能，另一些则提出了各种增强技术。尽管有这些研究结果，但在一些情况下，使用经典反向积分法提取的能量衰减曲线及其计算出的参数似乎并不总能代表所研究的现象。其中包括早期衰减取决于紧接直达波之后出现的强烈、清晰反射的情况，就像大多数意大利歌剧院那样。其他情况是测量到的脉冲响应信噪比非常低或缺少直达波。在文献中，已经提出了施罗德方法的替代方法，从希尔伯特变换到非线性处理技术。在这项工作中，提出了一种基于预处理能量检测的包络提取方法，用于早期衰减估计。结果表明，即使在非线性情况下，该方法也能返回与衰减第一部分非常匹配的包络，从而给出关于衰减第一部分的详细信息。针对在历史悠久的歌剧院中测量的一些示例性脉冲响应，展示并讨论了所提方法的性能。最后给出了该方法感知相关性的初步研究。
