Precedence Effect for Specular and Diffuse Reflections

Acta Acustica 2021, 5,1 Ó F. Wendt & R. Höldrich, Published by EDP Sciences, 2021 https://doi.org/10.1051/aacus/2020027 Available online at: https://acta-acustica.edpsciences.org SCIENTIFIC ARTICLE Precedence effect for specular and diffuse reflections Florian Wendt* and Robert Höldrich University of Music and Performing Arts Graz, Austria, Institute of Electronic Music and Acoustics, Inffeldgasse 10/3, 8010 Graz, Austria Received 26 May 2020, Accepted 3 November 2020 Abstract – Studies on the precedence effect are typically conducted by presenting two identical sounds simulating direct sound and specular reflection. However, when a sound is reflected from irregular surface, it is redirect into many directions resulting in directional and temporal diffusion. This contribution introduces a simulation of Lambertian diffusing reflections. The perceptual influences of diffusion are studied in a listening experiment; echo thresholds and masked thresholds of specular and diffuse reflections are measured. Results show that diffusion makes the reflections more easily detectable than specular reflections of the same total energy. Indications are found that this mainly due to temporal diffusion, while the directional diffusion has little effect. Accordingly, the modeling of the echo thresholds is achieved by a temporal alignment of the experimental data based on the energy centroid of reflection responses. For the modeling of masked threshold the temporal masking pattern for forward masking is taken into account. Keywords: Echo suppression, Sound source localization, Room acoustics, Spatialization 1 Introduction precedence; increased echo threshold delays imply a stronger echo suppression and consequently a stronger precedence The precedence effect refers to a group of perceptual effect. phenomena which allow us to localize sound sources in Many investigations have contributed to our under- challenging reverberant environments. Research has shown standing of the precedence effect by measuring the echo that the auditory system differently weights the spatial cues threshold with reflections that are identical to the direct over the stimulus duration; the sound source direction is sound (see [1, 2] for reviews). However, such specular reflec- determined mainly by the onset of the stimulus, where tions represent rather artificial conditions, which require an localization cues of the direct sound prevail. Corresponding infinitely large, flat, rigid reflecting surface [3]. When the studies typically utilize a two-source paradigm, representing sound encounters a real-life wall, it is inevitably redirected a leading direct sound and a lagging specular reflection at also into angles other than the specular reflection angle. the same intensity. The parameter of interest for this setup There are only a handful of contributions which studied is the lead-lag delay. For very short delays between direct the precedence effect in more realistic scenarios using wall sound and reflection below 1 ms, summing localization panels for creating the reflection, e.g. [4–6]. occurs and the two sounds appear as a single fused image This contribution examines how reflection properties of located between the sound instances. As the delay slightly a wall influence the echo suppression for pulsed noise exceeds the limits for summing localization the precedence signals. First, an overview on the relevant literature is given effect becomes active. In this range the auditory system in Section 2. Subsequently, Section 3 presents a simulation suppresses localization cues carried by reflections and the for diffuse reflection responses based Lambertian reflection. leading direct sound dominates the perceived location of a The simulation considers both temporal and directional single auditory image. Another increase of the delay yields diffusion of the reflected sound by incorporating the scatter- widening of the auditory image until it breaks apart at the ing coefficient. The perceptual influences of diffuse reflec- upper limit of echo suppression. At this transition, the tions are studied in a listening experiment. Section 4 so-called echo threshold the reflection becomes audible as a outlines the experimental design for measuring the echo second auditory image. This threshold is especially relevant threshold and the masked threshold. The experimental because it can be used to determine the strength of results are discussed in Section 5. Modeling attempts of the results of both thresholds are presented in Section 6. Section 7 relates the findings to previous studies and *Corresponding author: [email protected] Section 8 summarizes the contribution. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 F. Wendt and R. Höldrich: Acta Acustica 2021, 5,1 2 Echo suppression for non-specular Lokki et al. [14] studied the qualitative influence of the reflections temporal diffusion of reflections and found significant perceptual differences. In contradiction to [12]and[13], Specular reflections represent one of two extreme condi- they assumed that the clear and open acoustics reported tions which have been identified for rigid surfaces. When for specular reflections is due to stronger precedence, the direct sound of a source is reflected specularly, both compared to temporal diffuse reflections that render the magnitude spectrum and phase spectrum are maintained sound weak and muddy. and the sound bounces off the surface with the same angle as it encountered the surface. The other extreme condition is the diffuse reflection that occurs when the reflected 3 Simulating diffuse reflections energy is scattered [3, 7]. It yields a reflected sound that spreads directionally and temporally. A specular reflection occurs when a plane wave is In room acoustics, reflections on rigid walls are typically reflected on an infinitely large, smooth, and rigid wall. approximated by dividing the reflected energy into two Snell’s law for the specular reflection states that angle of components, specular and diffuse, with the scattering reflection is equal to the angle of incidence. The impulse coefficient s defining the ratio of the scattered energy to response of such a reflection is described by a Dirac delta d À the total energy reflected by the surface. Thus, the scatter- distribution (t Tr)withthedelayTr calculated from ing coefficientisdefined in the interval s = [0, 1] and a value the distance between the corresponding image source and of 1 corresponds to a fully diffuse reflection with no specular the receiver. reflection component. For simulating a diffuse reflection, suppose the point While many psychoacoustic experiments have con- source S in Figure 1 emits a short power impulse at time tributed to our understanding of the precedence effect t = 0, represented by a Dirac delta function d(t) with unity with specular reflections, knowledge on the influence of energy. The sound power dPW(t) reaching the wall element h spatio-temporal diffuse reflectionsisstillroughandpartly dW by the angle of incidence S and distance rS is then contradictory. The temporal diffusion for example yields defined by, spectral colorations of the reflection. According to h P ðtÞ¼cos S dðt À t Þ W ; ð Þ Blauert and Dinveyi [8] suppression occurs for any natural d W 2 S d 1 4p rS reflection where the spectrum of the lag contains exclusively qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi those regions that are present in the spectrum of the lead. 2 2 2 with rS ¼ x þ z þ d , time t = r /c, and speed of However, for reflections differing in magnitude spectrum S S S sound c. Diffuse reflections are typically interpreted and phase spectrum, the suppression was found to be fl generally weaker compared to a specular reflection, e.g. by assuming Lambertian re ection in which the scattered sound power from the element dW is proportional [8–10]. to the cosine of the angle of reflection cos h [3]. The Robinson et al. [11]studiedtheinfluence of temporal R intensity dIW reflected by the wall element dW of a diffusion on the echo threshold delay by modeling visual fl fl perfectly re ective wall without absorption that reaches observations of measured re ection responses from diffu- the receiver R is defined by, sors. Their simulation approximates the impulse response of diffuse reflections by multiplying Gaussian white noise cos hS cos hR I W ðÞ¼t dðÞt À tSR W ; ð Þ d 2 2 d 2 with the envelope describing the probability density func- 4p rS rR tion of a gamma distribution. Resulting echo threshold qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2 þ 2 þ 2 delays, defined by the temporal energy centroid of impulse with rR x z dR and tSR =(rS + rR)/c. Assum- responses, revealed mostly no difference between the sup- ing the reflected sounds of wall elements dW to be fl pression of compact and a temporal diffuse re ections. incoherent, the overall intensity Idiff reaching the Grosse et al. [12] studied the perceptual influence of receiver R is obtained by the integration over both directional diffusion of either direct sound or reflection by dimensions of the wall, presenting the sound from a single loudspeaker or by pre- ZZ cos hS cos hR senting mutually uncorrelated versions of similar sounds I ðtÞ¼ dðt À tSRÞ x z: ð Þ diff 2 2 d d 3 4p rS rR from nine adjacent loudspeakers. Although no pure specu- W lar lead/lag condition was tested in their experiments, there is evidence that the directional diffusion of the reflection The two cosines can be replaced by distance relations might reinforce the echo suppression and for both speech cos hS = dS/rS and cos hR = dR/rR, yielding the elliptical and noise bursts, the echo threshold delay is longer if diffuse integral, reflections are used. ZZ dS dR Visentin et al. [13] recently studied the influence of an I ðtÞ¼ dðt À tSRðx; zÞÞ dxdz; ð4Þ diff p r3ðx; zÞ r3 ðx; zÞ fl fl 4 S R early re ection on spatial attributes by employing real at W and diffusive wall panels.

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