Extraction of the envelope from impulse responses using pre-processed energy detection for early decay estimation

Abstract

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.

The influence of signal type on perceived reverberance

“…Methods of calculating RT have evolved over time to account for the complexity of IRs [e.g., DeCesaris et al (2015)], but still begin with an impulsive sound. These responses represent reverberation decay in the room after a signal's end, and are calculated by deconvolving an impulsive sound from a measurement of that sound in the room.…”

Energy Criteria in Italian Opera Houses a Survey Over 11 Theatres

“…Two monaural criteria were chosen and related to the early reflections distribution: early decay time EDT and sound strength G. These criteria are analysed in the stalls area in the frequency range 500 -2000 Hz. EDT is computed using the pre-processed energy detection method 3,4 , which allows a better definition on the early decay as will be pointed out in the following. G is calculated with a code written ad hoc, where the denominator is built as an energetic average of six IRs measured at 1 m from the dodecahedron, windowed over 10 ms and brought back to 10 m using a logarithmic difference 5 .…”

UWB Channel Impulse Responses for Positioning in Complex Environments: A Detailed Feature Analysis

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