Echo Density.Pdf

Audio Engineering Society Convention Paper Presented at the 121st Convention 2006 October 5{8 San Francisco, CA, USA This convention paper has been reproduced from the author's advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be nd obtained by sending request and remittance to Audio Engineering Society, 60 East 42 Street, New York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the Journal of the Audio Engineering Society. A Simple, Robust Measure of Reverberation Echo Density Jonathan S. Abel1;2 and Patty Huang2;3 1Universal Audio, Inc., Santa Cruz, CA, 95060, USA 2Center for Computer Research in Music and Acoustics (CCRMA), Stanford Univ., Stanford, CA, 94305, USA 3Laboratory of Acoustics and Audio Signal Processing, Helsinki Univ. of Tech., Espoo, FI-02015 TKK, Finland Correspondence should be addressed to Jonathan S. Abel ([email protected]) ABSTRACT A simple, robust method for measuring echo density from a reverberation impulse response is presented. Based on the property that a reverberant field takes on a Gaussian distribution once an acoustic space is fully mixed, the measure counts samples lying outside a standard deviation in a given impulse response window and normalizes by that expected for Gaussian noise. The measure is insensitive to equalization and reverberation time, and is seen to perform well on both artificial reverberation and measurements of room impulse responses. Listening tests indicate a correlation between echo density measured in this way and perceived temporal quality or texture of the reverberation. 1. INTRODUCTION tically, and the impulse response would arguably be indistinguishable from Gaussian noise with an evolv- Sound radiated in a reverberant environment will ing color and level [1]. interact with objects and surfaces in the environment to create reflections. These propagate and sub- The rate of echo density increase has to do with fac- sequently interact with additional objects and sur- tors such as the size and shape of the space and faces, creating even more reflections. Accordingly, whether it is empty or cluttered with reflecting ob- an impulse response measured between a sound jects. Although it has not been widely studied in the source and listener in a reflective environment will literature, echo density and its time evolution are record an increasing arrival density over time. After commonly thought to influence the perceived time- a sufficient period of time, the echo density will be so domain timbre of a space, with a large, rapidly in- great that the arriving echoes may be treated statis- creasing echo density being desirable. Abel AND Huang Reverberation Echo Density In [2], the variance over time of reverberation im- sliding impulse response window, the echo density pulse response energy (which can be indicative of measure presented here simply counts the number echo density) was seen to correlate with the subjec- of taps outside the standard deviation for the win- tive texture of late reverberation. In another recent dow, and normalizes by that expected for Gaussian work [3], temporal correlations in reverberation im- noise. pulse response frequency bands were shown to re- Reflections arriving separated in time or in level late to the \temporal color" of the reverberator. skew the tap histogram away from its limiting Gaus- The idea was that noise-like segments of a rever- sian form, and the percentage of taps outside a stan- beration impulse response would maintain small au- dard deviation is a computationally simple indicator tocorrelation sidelobes compared to their peak val- of this skew. In this way, the measure is normalized, ues, whereas segments with undesirable periodicities producing values on a scale from zero to around one. would have relatively larger sidelobes. The presence of a few prominent reflections results In the context of developing an artificial reverber- in a low echo density value, since they contribute ator based on pseudorandom sequences of echoes to a larger standard deviation and consequently a [4, 5], Rubak and Johansen cited literature and pre- smaller number of samples classified as outliers. By sented listening tests suggesting that reverberation contrast, an extremely dense pattern of overlapping impulse responses maintaining echo densities greater reflections approximating Gaussian noise will pro- than about four thousand echoes per second may duce a value near one. be treated statistically and sound similar to one another, independent of their actual echo densities. The proposed echo density measure is described in 2. The performance of the measure is examined Echo or reflection density has more commonly been inx 3 by computing echo density profiles of room expressed in terms of the number of reflections per impulsex response measurements and artificial rever- second. However, this measure is not always mean- beration generated by a feedback delay network re- ingful because it is unclear how to best define a reverberator with various amounts of state mixing. 4 flection, and sampling rate becomes a limiting fac- concludes the paper with a discussion about prop-x tor in counting reflections. As an estimate of reflec- erties of the echo density measure and how it may tion density in a given synthetic reverberator im- be useful in describing the temporal quality of rever- pulse response window, Griesinger suggested count- beration. ing echoes within 20 dB of the window maximum [6, pg. 192]. This method was used to measure echo 2. ECHO DENSITY PROFILE density in [7], where an echo was defined as an impulse response peak|impulse response taps larger in 2.1. Echo Density Measure absolute value than either of their neighbors. One Over a sliding reverberation impulse response win- difficulty with this approach is that any given reflec- dow, the proposed echo density measure η(t)|called tion can produce a large number of impulse response here the echo density profile|is the fraction of im- peaks, depending on the details of its propagation as pulse response taps which lie outside the window well as factors such as impulse response equalization standard deviation: [6, pg. 188]. In addition, the level of the loudest tap, t+δ and therefore the number of taps considered reflec- 1=erfc(1=p2) tions, is sensitive to the phase of its associated re- η(t) = 1 h(τ) > σ ; (1) 2δ + 1 fj j g flection and other characteristics which are not likely τ=t−δ X psychoacoustically meaningful. where h(t) is the reverberation impulse response (as- In this paper, the problem of measuring echo den- sumed to be zero mean), 2δ +1 is the window length sity as a function of time is considered. The ap- in samples, σ is the window standard deviation, proach taken follows from the fact that once the 1 room or reverberator is sufficiently mixed, the im- t+δ 2 1 pulse response taps take on a Gaussian distribution, σ = h2(τ) ; (2) 2δ + 1 irrespective of the actual reflection density. Over a " τ=t−δ # X AES 121st Convention, San Francisco, CA, USA, 2006 October 5{8 Page 2 of 10 Abel AND Huang Reverberation Echo Density 6 7 8 1 5 0.8 0.6 4 0.4 0.2 2 3 amplitude / echo density 1 0 −0.2 1 2 3 10 10 10 time − milliseconds 1 2 3 4 5 6 7 8 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 occurrence rate 0 0 0 0 0 0 0 0 −2 0 2 −2 0 2 −2 0 2 −2 0 2 −2 0 2 −2 0 2 −2 0 2 −2 0 2 amplitude amplitude amplitude amplitude amplitude amplitude amplitude amplitude Fig. 1: Top: Measured room impulse response (red, near bottom, 44.1 kHz samples) and its echo density profile (green, near top). Note that the time axis is on a logarithmic scale. Bottom: Window histograms centered at times indicated by the blue circles in top plot. The Gaussian distribution is indicated by a green line. Normalized occurence rates greater than 2.0 are plotted at this value. 1 is the indicator function, returning one when with 1 {·} 2 its argument is true and zero otherwise, and t+δ : 2 erfc(1=p2) = 0:3173 is the expected fraction of sam- σ = w(τ)h (τ) (4) "τ=t−δ # ples lying outside a standard deviation from the X mean for a Gaussian distribution. and where w(t) is normalized to have unit sum τ w(τ) = 1. The echo density profile is more generally computed Consider the impulse response shown in Figure 1, using a positive weighting function w(t) so as to de- P measured in the lobby of the Knoll, a building at emphasize the impulse response taps at the sliding Stanford University. (This impulse response is also window edges: used in Figures 2{5.) The direct path is evident, t+δ as are a number of early reflections giving way to a 1 η(t) = w(τ)1 h(τ) > σ (3) noise-like late field response. Also shown is the echo p fj j g erfc(1= 2) τ=t−δ density profile, η(t), computed according to (1) using X AES 121st Convention, San Francisco, CA, USA, 2006 October 5{8 Page 3 of 10 Abel AND Huang Reverberation Echo Density a 20 ms long sliding window, and tap histograms for 3 several of the windows used in computing the echo 2.5 density profile. 2 The echo density profile starts near zero and in- 1.5 creases over time to around one, where it remains echo density 1 for the duration of the impulse response.

Load more