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

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.

A comparison of methods to compute the "effective duration" of the autocorrelation function and an alternative proposal.

The "effective duration" of the autocorrelation function (ACF), τ(e), is an important factor in architectural and musical acoustics. For a general application, an accurate evaluation of τ(e) is relevant. This paper is focused to the methods for the extraction of τ(e) values from the ACF. Various methods have been proposed in literature for the extraction of the τ(e) from a given signal, but these methods are not unambiguously defined or may not work properly in case of particular signals. Therefore, the general use of these methods may sometimes give rise to questionable results. In the present work, the methods existing in literature for extracting τ(e) are analyzed, their advantages and drawbacks are summarized, and finally an alternative method is proposed. The proposed algorithm is compared to those found in previous literature, applying them on the same sound signals (classic literature references and other ones publicly available on the Internet). It is shown that the results obtained with the proposed method are consistent with the results of the previous literature; moreover the proposed method may overcome some of the limitations of the existing methods.