PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Room acoustic texture: a methodology for its quantification
Alejandro Bidondo1; Leonardo Pepino2
1

UNTREF University, Argentina

2

UNTREF University, Argentina

ABSTRACT
Room acoustic texture is defined by Beranek as the subjective impression listeners derive from the temporaland amplitude patterns of early reflections, at the receiver’s locations inside the room. Traditionally, room
acoustic texture was qualified by visual inspection of the room impulse responses (RIR) or counting
reflection´s peaks. Taking into account that the reflections in the later part of the RIR follow a Gaussian
probability distribution and are totally mixed, we define the early reflections as every amplitude outlier
present in a RIR, and mixing time as the instant when their cumulative energy reaches 99% of their totalenergy. To find outliers amplitudes, we proceeded to cancel the decay of the energy time curve (ETC) underanalysis using a mobile median filter. Then, the particular echo density function (edf) is defined as the
decay-cancelled outliers cumulative energy, over time. From this processing, a group of descriptors were
defined that jointly describe the room acoustic texture, at one point in the sound field. Among thesedescriptors are the mixing time, expected texture and distance between models. Applications of thesedescriptors and their spatial standard deviation in rooms seem to be very broad, describing their temporalfine-structure.
Keywords: Acoustic texture, Early reflections.

1. INTRODUCTION
The acoustic texture of a room was defined by Beranek: “Texture is the subjective
impression that listeners derive from the patterns in which the sequence of early soundreflections arrive at their ears. In an excellent hall those reflections that arrive soon after
the direct sound follow in a more-or-less uniform sequence. In other halls there may be aconsiderable interval between the first and the following reflections. Good texture
requires a large number of early reflections, uniformly but not precisely spaced apart, andwith no single reflection dominating the others” (Beranek, 1996).
“Sound radiated in a reverberant environment will interact with objects and surfaces in
it to create reflections. These propagate and subsequently interact with additional objects
and surfaces, creating even more reflections. Accordingly, an impulse response measured
between a sound source and listener in a reflective environment will record an increasing
arrival density of reflections over time. After a sufficient period of time, the echo density
will be so great that the arriving echoes may be treated statistically, and the impulse
response would arguably be indistinguishable from Gaussian noise with an evolving colorand level” (Jot, 1997).
Regardless of being able to assess the importance of early reflections, separating themfrom a Room Impulse Response (RIR) has been the subject of many investigations,sometimes questioning the need to clearly identify the room in which the listener is(Kahle, 2018).
The aim of this research is to develop a method to efficiently separate early reflections
1
2

abidondo@untref.edu.ar
leonardodpepino@gmail.com

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(ER) from the rest of a RIR reflections, and study their amplitude and temporal
distribution to develop a set of parameters describing the acoustic texture at one point
inside a sound field.
2. PREVIOUS STUDIESAs expressed in (O´Donovan, 2008), room acoustics is generally evaluated in terms ofvarious subjective characteristics that expert musicians / listeners assign to sound received
at a location in space such as liveness, intimacy, fullness / clarity, warmth / brilliance,
texture, blend, and ensemble. Most of these criteria are related to the room impulse
response produced with the excitation of sound sources (usually from speakers on stage, or
distributed in the hall), registered at several receiver or listener locations.
Several studies proposed to quantify the acoustic texture of a RIR: In (Hidaka, 2008) an
acoustic texture parameter is defined as the number of peaks with amplitude higher than
the threshold of absolute perceptibility (aWs curve) of a single reflection vs. delay time formusic (Schubert, 1961), in the first 80 ms of RIR. This method uses Hilbert transformationfor envelope extraction. In (Paskaš, 2010), the author used fractal dimension toquantify texture.
The acoustic texture would express the degree of direct sound coloration, sound source
localization modification and, if reflections are coming from lateral directions, acoustic
source width (ASW) changes. Regardless of considering these phenomena as acoustic
distortion or not, they should be able to be identified and quantified, to finally analyze
their uniformity in different areas of a sound field, all these from a RIR. From theseprevious statements, can be deduced that: a) there could be an “ideal” texture, b) that
texture is a matter of early reflections, and c) a criteria for deciding which reflections are
considered “early” is needed.
As described by J. D. Polack (Polack, 1988), impulse responses are Gaussian processes,
provided that global analysis is carried out on hand of a proper model of impulse
responses. In this process, it is essential to discard the early part with strong reflections,and the very late part which simply is background noise. Finally, the reverberation tailexhibits a gaussian distribution of amplitudes in function of time, decaying exponentially.
Abel (Abel, 2006) mentions room impulse response texture as a descriptor forreverberation quality and proposed methods to visualize the echo density profile (EDP) of
a RIR, and detect outliers from a gaussian distribution, considering every outlier as an
early reflection. He also expressed that the temporal quality of artificial reverberators,
analysed through their impulse responses, is strongly correlated to the diffusion settings
used to generate them. From Abel´s work (Abel, 2007), the reverberation resulting from a
diffusion setting of 0.2 was described as “crackly” or “sputtery,” while the reverberation
resulting from the highest diffusion setting showed to has a smooth acoustic texture,described subjectively as “smooth” or “windy”.
Abel et al also said: “Traditional acoustical parameters for reverberation (ISO 3382,
2012) have not included measures related to reflection density or the description of
temporal timbre, but the time-domain quality or texture of a reverberant signal can be as
varied and audible as the (frequency- dependent) reverberation time. Since the echodensity measure is able to discriminate so well between different diffusion settings and theresulting rate of echo density increase, it has much potential as a tool for evaluating thetime-domain timbre of reverberation.”
Considering the lack of metrics to quantify room acoustic texture, a set of descriptors
are proposed. In order to find meaningful descriptors, early reflections are identified,isolated and processed from the room impulse response information.

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3. ROOM IMPULSE RESPONSE TEXTURE MODEL
3.1

Acoustic Texture

As defined in (11), texture is:• the physical feel of something — smooth, rough, fuzzy, slimy, and lotsof descriptions something in between.
• the physical composition of something (especially with respect to the size andshape of the small constituents of a substance).
• the essential quality of something.
As time evolves, every RIR is composed by the direct sound, a group of reflections
named “early reflections”, and after those, the “late reflections”. The instant of separation
between both is named Mixing time (Mt). After Mt, the reverberation tale can beconsidered an exponentially decay of gaussian white noise. The particular temporal
distribution and amplitudes of this early reflections reflect the room acoustic texture. In
this research we quantify the texture of a RIR as the comparison of the shape of thetemporal evolution curve of the room´s dynamic system early reflections cumulative
summation, with the shape of an “ideal” or “expected” case. This calculation is madebetween the initial time delay gap (ITDG) and Mt. Around these considerations, a set ofdescriptors can be defined - globally and over third octave bands -, which describe thetemporal evolution of the early sound field.
3.2

Echo density function - edf

In this study, an efficient method to compute the energy density function (edf),
detecting every amplitude outlier in a RIR and constructing a function from the cumulative
sum of their energies over time was developed.
For this, considering every amplitude outlier as an ER, a new definition of Mt is
proposed: the instant when the cumulative outliers function has reached 99% of its
maximum. In this sense, while we cannot talk about ergodicity (12), this proposal
complies with the mathematical definition of mixing - time required by a Markov chain forthe distance to stationarity to be small (Levin, 2017) - and, consequently of course, with amemoryless state - because all direction information is carried out just in the outliers,
which have fade out or disappeared after Mt - (Lindau, 2010). As the analysis process
takes place in a RIR, instead of referring to local temporal diffusion, we propose thequantification of the texture of the RIR, analized in the 0 : Mt time interval.
To detect all outliers reflections, a median moving filter (MMF) was used with awindow length related to the minimum frequency of the first third octave frequency band
under analysis, as described by eq. 1. The median is just the middle value in a distribution,and it is less influenced by the outliers, as opposed to the mean that can be "dragged" up or
down by extreme values (13).
For a reflection to be outlier in our case, its amplitude has to stand out with respect tovalues close in time. The method includes a decay subtraction to the RIR under analysis
and normalization, relative to the total summation of the outliers energies.
eq. 1.
Where:
Wd is the MMF window duration,
fmin is the minimum frequency of the first third octave band under analysis,

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fs is the sampling frequency.
The median moving filter was applied to the energy time curve (ETC), as is describedby eq. 2 (also see Figure 1).
eq. 2.

Figure 1. Blue line: Room’s Energy Time Curve (ETC) of a generic RIR. Red line: median moving filter
result applied to the ETC.

Afterwards, the Decay - cancelled Early Reflections (DcER) was obtained as describedby eq. 3.
eq. 3.
And the echo density function, edf, from the RIR under analysis, is obtained by eq. 4.

eq. 4.
Where:RIR (t) is the room impulse response.
RIRMedian is the room impulse response after the MMF processing.
DcER: are the Decay-cancelled Early Reflections or outliers, over time.
Actual edf(t): is the calculation applied on the actual RIR under analysis.
edf (t): generally speaking, is the echo density function.
Synthetic RIRs were generated from exponentially decaying gaussian white noise withdifferent RT60s. These signals were devised with constant and evolving echo density, andwere used to test the proposed method. Both cases implied an absence of outlierreflections, resulting in a smooth edf. It was observed the cumulative energy of the outliers
follows eq. 5, and can be thought as a capacitor charging over time, as can be seen in figure
2. The generalized and ideal equation governing this behaviour is eq 5.
eq.5.

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Three edf’s were calculated for every RIR: One actual edf and two “reference” edf’s.
Actual edf: is the direct application of the eq. 3 on the actual RIR under analysis.
Ideal edf: For the first “reference” edf of eq. 4, a and b constants are adjusted using two
known values taken from the actual edf: the initial value of the function, t0, whichcorresponds to the initial time delay gap (ITDG) and Mt, where the actual edf (t) reaches
an amplitude of 0.99 from its final value. Also, third octave frequency filtering wasapplied to the actual RIR, finding Mt values over third octave frequency bands. This way,
the ideal edf, is established through the ITDG and actual Mt.
Expected edf: A second “reference” edf is calculated by best fitting eq.4 to the actualedf.
Once the models are attained, the curves are displayed in a log(t) scale.
In figure 2, resulting curves at 1 KHz frequency band are shown with some of theassociated texture descriptors.

Figure 2. Resulting edf curves from the texture calculation for 1 KHz frequency band of a very renowned
local Opera Theater. RIR (audience area). Observing the actual edf curve, deviation from the smooth growthof the expected edf can be seen. Expected texture (ETx) is the Pearson correlation coefficient between theactual edf and the expected edf. DBM is the Bhattacharya distance between expected edf and ideal edf curves.
Associated numerical results are: ETx = 0.1815, DBM = -2.93, Ctr = 44.67 ms, Mt = 176 ms.

For the case of synthesized gaussian white noise RIRs, the ideal edf, expected edf andactual edf are coincident, as can be seen in figure 3. No considerably irregularities appear
in the actual edf due to non-existence of early reflections. We refer to this type of cases,
the perfectly distributed ER over time, with outliers amplitudes not disturbing the soundfield.

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Figure 3. Actual edf (black line), Ideal edf (blue line) and Expected edf (dashed line) computed on a fullbandwidth gaussian white noise synthesized RIR. Early reflections in red. In this case, Expected Texture =0.999 and DBM ≌ 0.

3.3

Texture of a RIR

As acoustic coatings, particularly diffusers, are added, placed and distributed inside aroom, the RIR’s actual edf curve changes, and tends to move to the origin (t=0);
simultaneously an expected mixing time (EMt) is estimated through the expected edf. If itschange is uniform throughout this process - constructing a curve without irregularities
from t = ITDG to Mt, resulting in a high value of ETx -, which sometimes means a uniform
spatial distribution of acoustic coatings (because this means a uniform spreading of theacoustic energy in time), Mt finally gets effectively reduced compared to the lessacoustically treated state.
As this “building process” of the actual edf happens, it is possible to measure thedistance between the ideal edf and the expected edf, DBM, the autocorrelation duration of
the RIR, Ctr [ms] (Bidondo, 2016), as well as the instantaneous texture that the actual edf
is showing, compared with the ideal and the expected edf´s.
Expected Texture (ETx) is defined as the Pearson correlation coefficient between theactual edf and the Expected edf, as stated by eq. 6.

eq. 6
Where:
r: is the Pearson’s coefficient of correlation.
cov: the covariance between variables.
𝜎: standard deviation of the variable.
The same concept is valid for the Texture (Tx), defined as the Pearson correlation

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coefficient between the actual edf and the ideal edf.
The distance between models (DBM) is the Bhatthacharyya distance between the ideal
and the expected edf models. A positive sign in the result means the ideal edf curve is after
the expected edf curve. A negative sign in the result means the ideal edf curve is before theexpected edf curve. In both cases, it is desirable that DBM be small.
As ETx and Tx values were found to be mainly between 0.8 and 1, it was decided todisplay
to get a spread between 0 and 1. An
is obtained for the synthetic
gaussian white noise RIR, indicating that the regression predictions almost perfectly fit
the data, as can be seen in Figure 3.
4. RESULTS
Third octave calculation over real RIRs showed different Mt, ETx and DBM results.
By modifying the median moving filter window size, evidence showed it has little or noeffect in the results.
By analyzing synthesized RIRs through a neural net model, it was found ETx is directly
affected by diffusion and RT, and inversely affected by room’s volume [m3]. On the other
hand, DBM is inversely affected by diffusion and EDT, and directly affected by room’s
volume [m3].
Maximum correlation between the real edf and the expected edf means an almost ideal
diffusion for the exhibited expected mixing time, which in turns should coincide with theideal edf mixing time.
5. CONCLUSIONS AND FUTURE WORK
A simple and efficient calculation method to find the early reflections and the mixing
time was presented. It was also presented an ideal temporal evolution curve for the
diffusion process of a room considering it as a dynamic system, and the description andquantification of the room acoustic texture through several descriptors. Global and thirdoctave frequency bands results of the proposed descriptors could give information about
the need of acoustic diffusers and / or EDT and / or RT modification, and may allow toknow those bands outside of "targeted" (ETx, DBM, Mt) values.
Future work includes studying how diffusers surface and their location inside a room
modify the actual edf function and their associated parameters. Also, a study of theacoustic texture is needed for every type of room.
6. DISCUSSION
Evidence curiously shows high similarity between this dynamic acoustic process(temporal evolution of early reflections carrying directional information) and thefacilitated diffusion process in biology, and diffusion processes in chemistry.
In preliminary studies it was observed that both ETx and DBM are sensitive to RT,
EDT, room volume, sound field diffuseness and location of the sound source, in different
proportions, being able to use them to evaluate the acoustic texture characteristics of themeasurement point. This descriptor´s behaviour may led to measure the sound field
diffuseness with DBM and to evaluate the balance between room volume [m3], EDT [s]and sound field diffuseness with ETx. May this balance show that large values ofscattering coefficient are not necessarily reflected in the texture of the sound field?
The acoustic expected texture (ETx) is inversely proportional to the Volume [m 3], anddirectly proportional to EDT [s], RT [s] and the diffuseness of the sound field. Acoustic
expected texture is also sensitive to the spatial distribution of the acoustic coating. It wasalso observed that as diffusion of the sound field increases, for constant room volume,

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EDT and RT, ETx gets maximized, Mt diminishes, and DBM tends to zero. Also, whenideal and expected edf curves tend to coincide, acoustic “distortion” would diminish, andcould be a numeric, objective target for room acoustic designs.
Faced with this evidence, it would seem appropriate to propose that (temporal)
diffusion would not be a state but a process; for that reason it would not be correct to look
for a certain amount of diffusion, but a certain development of it in time.
ACKNOWLEDGEMENTS
Authors may acknowledge financial and infrastructure support to UNTREF University.
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