High Reverberation Research Articles

Ultrabroadband sound control of 3D spaces using plasmacoustic metalayers

Controlling sound in three-dimensional spaces is a complex task, challenged by the intricacies of acoustic modal structures, the variety of noise sources, and the propagation of waves. This research analyzes the influence of local impedance control on the global sound field within a parallelepipedal volume characterized by high reverberation. The employed electroacoustic transducer is based on a corona discharge mechanism and utilizes the Plasmacoustic Metalayer concept. The sound field is regulated directly by the interaction between the air particles and the ionized air produced in the discharge area. The inertia-free plasmacoustic Metalayer contributes to an increased control bandwidth. Experimental tests conducted with several actively controlled transducers distributed throughout the volume demonstrate the dampening of multiple modes. This leads to a more consistent frequency response and a broadband reduction in sound pressure levels across the entire space, demonstrated here up to 700 Hz. Numerical simulations suggest that such a systemcan also be potentially efficient in a more realistic space such as a vehicle cabin.

SA-UCBSS: Sparsity-Based Adaptive Underdetermined Convolutive Blind Source Separation

Blind source separation is the process of separating unknown source signals based only on the received mixing signals when the source signal cannot be accurately known. Traditional methods are mainly based on linear approximate transformation models that often have large systematic errors in high reverberation environments, resulting in poor separation performance. To avoid these limitations, a sparsity-based adaptive underdetermined convolutive blind source separation (SA-UCBSS) algorithm is proposed by unifying a convolutive approximate transformation model and an Lp(0<p≤1)-norm regularisation penalty. A crosstalk canceller is designed for room impulse response pretreatment with p-norm optimisation to eliminate audible echoes, and a sparse optimisation scheme is designed for the parameter initialisation to accelerate the convergence of the iterative recovery process. Subsequently, a convolutive approximate transformation model is built to achieve a more accurate estimation of the mixing system. The SA-UCBSS algorithm is proposed to achieve better source separation by adaptively tuning the value of parameter p. Experimental results including BSS of the synthesised and live-recorded speech convolutive mixtures showed that the SA-UCBSS algorithm had superior separating properties and better robustness than several popular algorithms.

Room impulse response reshaping-based expectation–maximization in an underdetermined reverberant environment

Source separation in an underdetermined reverberation environment is a very challenging issue. The classical method is based on the expectation–maximization algorithm. However, it is limited to high reverberation environments, resulting in bad or even invalid separation performance. To eliminate this restriction, a room impulse response reshaping-based expectation–maximization method is designed to solve the problem of source separation in an underdetermined reverberant environment. Firstly, a room impulse response reshaping technology is designed to eliminate the influence of audible echo on the reverberant environment, improving the quality of the received signals. Then, a new mathematical model of time-frequency mixing signals is established to reduce the approximation error of model transformation caused by high reverberation. Furthermore, an improved expectation–maximization method is proposed for real-time update learning rules of model parameters, and then the sources are separated using the estimators provided by the improved expectation–maximization method. Experimental results based on source separation of speech and music mixtures demonstrate that the proposed algorithm achieves better separation performance while maintaining much better robustness than popular expectation–maximization methods.

Speech intelligibility in reverberation based on audio-visual scenes recordings reproduced in a 3D virtual environment

Audio-visual scenes were collected in a medium-sized reverberant conference hall through in-field 3rd-order ambisonics impulse response recordings and 360-degree stereoscopic videos. The visual scenes included cues of the room and the location of the sound sources, without lip-sync-related cues. Speech intelligibility tests based on seven audio-visual scenes were administered inside an immersive virtual 3D environment reproduced through a spherical 16-speaker array synched with a head-mounted display. Forty normal-hearing subjects were engaged to test the effects on speech intelligibility of a talker in front of the listener and amplified by two lateral symmetrical loudspeakers, in the case of (i) different listener-to-talker distances, (ii) one-talker noise at various azimuth angles around the listener, (iii) high reverberation with –5 dB signal-to-noise ratio, (iv) self-motion, and (v) visual cues. We conducted tests in four configurations, that is, audio-visual and audio-only, both with self-motion and in the static condition. The static audio-only tests scored the highest speech intelligibility, followed by a tie between audio-visual with self-motion and in the static condition. Speech intelligibility decreased as the target-to-listener distance increased in all the noisy scenes. Additionally, speech intelligibility increased when the noise azimuth was at 120° compared to both 180° and 0° , with the talker at approximately 8 m from the listener. The advantage of the spatial separation of the noise signal in reverberation is evident in the case of the audio-visual with self-motion test. This suggests a spatial release from masking in the presence of reverberation, one-talker-interfering noise and within an more ecological scene.

Acoustic measurements of Edzna: A Mayan archaeological place in Mexico

Over the years, numerous acoustic measurements have been made to examine archaeological spaces, providing valuable insights into how sound played a role in several cultures throughout history. This research found twenty-eight studies worldwide in the last seven years (2016 – 2022); twenty in Europe (e.g., Stonehenge in England or the Palace of Charles V in Spain); four in Asia (e.g., Rachmaninov Hall in Russia); three in America (e.g., Mexico City Cathedral in Mexico); and one in Africa (Iwan masjids in Egypt). However, there has been limited investigation into the acoustics of cultures in America such as the Incas, Aztecs, Mapuches, Patagones, or Guaranies. The Mayan zone, in particular the archaeological site of Edzna (Campeche, Mexico) is not an exception. This work presents a practical and portable acoustic measurement of this site to determine if the architectural spaces were designed considering sound effects. Edzna is organized in six main places: (1) Main Plaza, (2) Nohochna, (3) Great Acropolis, (4) Five-story building, (5) Small Acropolis and (6) Ballcourt. Acoustic measurements for this study were taken in the Main Plaza, the Great Acropolis, and the Small Acropolis. This study revealed that the archaeological zone presents high Reverberation Time (RT20) levels above 2 or 3 s. In particular, the RT20 of the Main Plaza (RT20 = 2.2 s on average), suggests that the space was used for crowded events where participants could listen around the plaza. In contrast, the Great and Small Acropolis (RT20 = 1.2 s on average) were probably used for private, more intimate events.

ACOUSTICAL ANALYSIS FOR THE LECTURE ROOMS IN UNIMAP

Acoustic analysis is a measurement used to analyse the behaviour of sound waves in enclosed spaces, which influences speech intelligibility. Another parameter that influences speech intelligibility is reverberation time. Reverberation time is the time for the sound source to decay by 60 dB. A high reverberation time causes sound to dissipate more slowly, resulting in continual reflection of sound waves, which disrupts student concentration in class. Furthermore, a poor acoustic environment could have an impact on health and lecture delivery. The objective of this study is to determine and analyse the acoustic performance for five selected lecture rooms in UniMAP. The reverberation time is the parameter of this study that was obtained from the Root Mean Square (RMS) of the sound pressure by using the impulsive sound source method from a burst balloon. In this study, the "balloon pop" sound pressure was consistently recorded at approximately 105dB across all cases. This measurement indicates the peak sound intensity of the stimulus. The influence of the location of receiver, design, and space volume for the lecture room on the reverberation time was investigated. At a location of 6 m from the sound source, at the back wall of a room with chairs, BKN 5 and BPU 5 measured longer reverberation times of 1.3 s and 1.2 s, respectively. The higher value of reverberation time is caused by where the sound receiver is. If it is close to a wall, the sound receiver will be exposed to numerous reflections of sound waves, causing the room to become reverberant. Compared to other lecture rooms, the length of BKN 5 and BPU 5 is shorter. Their lengths are 11.639 m and 11.689 m, so the sound receiver is closer to the wall and makes the reverberation time higher. BKN 5 room, which has a volume of 258.3 m3, had the highest reverberation time (1.2 s on average in a room with chairs). This is because it is larger than the other rooms. So, the reverberation times get longer as the room's volume increases. BPU 5 room had the longest reverberation time for a condition room without chairs (an average of 2.4 s), but it also had the smallest space volume (242.4 m3) compared to the other rooms. Thus, it takes longer for the sound waves in the room to fade away when there are no chairs there. If the smaller room didn't have enough sound-absorbing materials, the reverberation times would be longer.

A Wasserstein generative adversarial network with gradient penalty for active sonar signal reverberation suppression

Reverberation is the primary background interference of active sonar systems in shallow water environments, affecting target position detection accuracy. Reverberation suppression is a signal processing technique used to improve the clarity and accuracy of received signals by eliminating the echoes, reverberations, and noise that occur during underwater propagation. Existing reverberation suppression methods include algorithms based on Time-Frequency domain processing, noise reduction, adaptive filtering, and spectral subtraction, but their performance in high-reverberation environments (echo of small targets) still does not meet the requirements of target detection. To address the impact of high reverberation environments, we propose a structural suppression method based on the Wasserstein gradient penalty generative adversarial network (RSWGAN-GP). The reverberation suppression generation network uses a one-dimensional convolutional network structure to process normalized time-domain signals and achieves the reconstruction of the reverberation signal through Encoder-Decoder. The proposed method is verified through accurate and effective data collection during sea trials. Comparative results show that RSWGAN-GP effectively suppresses reverberation in observation signals with multiple bright spots, improving the signal-to-reverberation ratio by approximately 10 dB compared to other excellent algorithms and enhancing the information analysis and feature extraction capabilities of active sonar signals.

Unsupervised active sonar contact classification through anomaly detection

Target detection and sonar contact classification with active sonar systems are not trivial especially when operating in coastal and shallow water environments with multipath propagation, high reverberation and clutter. It is even more difficult when the sonar receiver is hosted on unmanned platforms with limited maneuvering capabilities unable to perform long-lasting tracking procedures. In such environments with high clutter density, real-time classification algorithms to discriminate target contacts from clutter contacts become crucial. This paper describes a method for active sonar clutter classification that exploits the large number of undesired contacts to learn the “fingerprint” of the environmental clutter and thus to identify the target contacts as anomalies. The paper introduces the method to obtain the features of detected sonar contacts from the beamformed signal of a triplet array of hydrophones that can be towed by an autonomous underwater vehicle. The paper also shows the performance of the proposed unsupervised classification algorithm with real data collected at sea and compares it to what has been achieved by using a convolutional neural network. The results show the capability of the proposed anomaly detection algorithm to properly deal with a variety of clutter contacts without requiring labeling of training data.

Premises for Effective Teaching and Learning: State of the Art, New Outcomes and Perspectives of Classroom Acoustics

Many booklets and standards have already been published on classroom acoustics in several countries, based on studies that were completed up to ten years ago and which were mainly focused on the speech intelligibility of pupils under noisy conditions. In the last decade many studies began to consider the complex speech communication scenario in classrooms, where acoustic requirements are needed for both teachers and pupils. The voice monitoring of teachers has revealed challenging conditions for speaking because of bad acoustics, with consequences on vocal health. Research has underlined the importance of voice support from the room, which has led us to reconsider the optimal reverberation time in classrooms, whose tendency is towards higher values than those for listening. On the other hand, it has been proven that a high reverberation increases the listening effort and decreases reading abilities. Thus, the question of the optimal reverberation time for speaking and listening arises, as well as the need to optimize the design of classrooms to support the voice and control the sound tail. The perceived reverberation is closely related to the perceived acoustical quality, which is recognized as the most important environmental aspect in classrooms. Reverberation also amplifies the noise produced by pupils themselves and affects their well-being. To cope with this, a new device has been introduced to inform pupils on the need to lower their voices and respect others. A summary of the state of the art of classroom acoustics is given in this lecture, together with the new findings on the effects of bad acoustics on pupils' learning and well-being and on teachers' vocal behaviour. A new paradigm on speech communication is needed in classrooms that should involve both teaching and learning. Further work is required to investigate the factors that underpin this complex communication scenario.

On data-driven underwater acoustic direct localization: Design considerations of a deep neural network-based solution

High reverberation, depth-dependent speed of sound and intricate environmental structures are a few of the challenges that make the development of reliable underwater acoustic localization (UAL) methods hard. Since the nontrivial physics of underwater acoustics and the inherent random effects amount to a highly complex statistical model of the measured data, it is natural to consider deep neural networks (NNs) as a central tool in the development of UAL methods. Indeed, recent studies have shown that some properly designed NNs can lead to unprecedented localization capabilities and enhanced accuracy. However, out of the already myriad available possibilities, it is not immediately clear how to choose a proper NN architecture—input structure, layer types, training procedure, loss function(s), etc.—that will lead to successful operation. In this talk, we will present an analytically informed architecture that can learn (for now, in simulations) to localize in complex underwater environments. We will also provide analytical arguments that can explain the robustness of such architectures to certain types of propagation/environment model mismatches. The operation of the discussed architecture will be demonstrated via simulation results in a rich, reverberant channel. The results suggest that deep NNs could become a viable solution to the UAL problem.

Electronic architecture—Improving room acoustics using time variant electro-acoustic systems

In 1990, we presented a technical paper at the Audio Engineering Society that described a new and unique system that enables microphones to be positioned as much as 50 feet from the sound source while producing high reverberation level without coloration from acoustic feedback. Since that time, hundreds of these systems have been installed throughout the world in both a wide range of applications, as well as wide variety of venues. We will discuss successful solutions for acoustical problems that are difficult to address using conventional architecture.

Subjective evaluation for sharp sound image construction based on reverberation control with surround sound system using parametric and electro-dynamic loudspeakers

3-D sound field reproduction systems can provide a high presence. These systems commonly use electro-dynamic loudspeakers. Electro-dynamic loudspeakers tend to construct diffuse sound images due to its wide directivity and high reverberation. In contrast, parametric array loudspeakers can construct sharp sound images due to its sharp directivity and low reverberation. On the other hand, it is difficult to provide reverberation presence by parametric array loudspeakers because of the sharp directivity. We have previously proposed a sharp sound image construction based on reverberation control with surround sound system using parametric and electro-dynamic loudspeakers. In this method, the sharp sound image is rendered using parametric array loudspeakers, and the reverberation presence is provided by electro-dynamic loudspeakers, emitting reverberation signals synthesized with reverberation control filters. Through the objective experiments, we have confirmed that this method can construct the sharp sound image with reverberation presence. In this paper, we conduct subjective experiments to confirm if the listeners can perceive the reverberation presence provided by the proposed method. In particular, we evaluated the sharpness and direction of the sound image, and the reverberation presence with objective and subjective evaluation experiments. From the subjective evaluation, we confirmed that the reverberation presence can be perceived.

DOA Estimation of Indoor Sound Sources Based on Spherical Harmonic Domain Beam-Space MUSIC

The Multiple Signal Classification (MUSIC) algorithm has become one of the most popular algorithms for estimating the direction-of-arrival (DOA) of multiple sources due to its simplicity and ease of implementation. Spherical microphone arrays can capture more sound field information than planar arrays. The collected multichannel speech signals can be transformed from the space domain to the spherical harmonic domain (SHD) for processing through spherical modal decomposition. The spherical harmonic domain MUSIC (SHD-MUSIC) algorithm reduces the dimensionality of the covariance matrix and achieves better DOA estimation performance than the conventional MUSIC algorithm. However, the SHD-MUSIC algorithm is prone to failure in low signal-to-noise ratio (SNR), high reverberation time (RT), and other multi-source environments. To address these challenges, we propose a novel joint spherical harmonic domain beam-space MUSIC (SHD-BMUSIC) algorithm in this paper. The advantage of decoupling the signal frequency and angle information in the SHD is exploited to improve the anti-reverberation property of the DOA estimation. In the SHD, the broadband beamforming matrix converts the SHD sound pressure to the beam domain output. Beamforming enhances the incoming signal in the desired direction and reduces the SNR threshold as well as the dimension of the signal covariance matrix. In addition, the 3D beam of the spherical array has rotational symmetry and its beam steering is decoupled from the beam shape. Therefore, the broadband beamforming constructed in this paper allows for the arbitrary adjustment of beam steering without the need to redesign the beam shape. Both simulation experiments and practical tests are conducted to verify that the proposed SHD-BMUSIC algorithm has a more robust adjacent source discrimination capability than the SHD-MUSIC algorithm.

Relationship Between Room Acoustics With Voice Symptoms and Voice-Related Quality of Life Among Colombian School and College Teachers During Online Classes in Times of COVID-19 Pandemic

AimTo determine the relationship between working conditions, especially room acoustics, with voice symptoms and voice-related quality of life among Colombian school and college teachers during online classes in times of COVID-19 pandemic.MethodExploratory cross-sectional study. Participants were thirty-two primary, secondary and university Colombian teachers, who were invited to fill in an online survey about working conditions and voice symptoms during online classes in times of COVID-19 pandemic. In the statistical analysis, four dependent variables and eight independent variables were defined. We used Generalized Linear Model with a Gamma distribution and Binary Logistic Regression to determine the association between voice with working conditions.ResultsHigh reverberation time and stress during online classes in times of the COVID-19 pandemic reduced slightly the VRQOL scores. For Factor 3 of the VFI, high reverberation time and months teaching online classes were associated at the multivariate analysis. Stress and years of experience were statistically associated with an increased odds of reporting hoarseness.ConclusionSimilar to pre-COVID-19, teachers with online classes during the COVID-19 pandemic are affected by two work-related factors namely high reverberation time and stress. These two factors are increasing their likelihood of reporting hoarseness and having lower voice-related quality of life, which may confirm the relationship between reverberation, stress, and voice also during online classes. This highlights the need of implementing workplace vocal and mental health programs to decrease the occurrence of voice problems among teachers in times of and post-COVID-19 pandemic.

Decoupled Multiple Speaker Direction-of-Arrival Estimator Under Reverberant Environments

Direction-of-arrival (DOA) estimation for multiple simultaneous speakers in reverberant environments is still one of the challenging tasks in the audio signal processing field. A recent approach addresses this problem using a spherical harmonics domain feature named <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">relative harmonic coefficients</i> (RHC). Based on a bin-wise operation across the STFT (short-time Fourier transform) domain, this method detects the direct-path RHC in the first stage, followed by single source localization in the second stage. However, the method is computationally expensive as each STFT bin requires an exhaustive grid search over the two-dimensional (2-D) directional space. In this paper, we propose a significantly more computationally efficient alternative that decouples the azimuth and elevation 2-D search to two separate one-dimensional (1-D) search. The proposed multi-speaker localization algorithm comprises of two main steps, responsible for: (i) achieving a joint direct-path RHC detection and decoupled DOA estimation using 1-D search; and (ii) counting the number of speakers and estimating their DOAs based on the estimates from direct-path dominated STFT bins. Experiments using both simulated and real-life reverberant recordings confirm the significant computational complexity reduction while achieving competitive localization accuracy, compared to the baseline approaches. Although our proposed method performs in an unsupervised manner, it proves to be applicable even under unfavorable acoustic environments with a high reverberation level (e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{60}=1$</tex-math></inline-formula> second).

Noise Control design for a Ventilation Fan - Case Study

A ventilation system was design and installed for a multi story garage. The ventilation system system had a vertical concrete shaft with the ventilation fan located on the top floor at street level. The ventilation fan is separated from the outside by a set of metal louvers. Adjacent to the louvers is an open pedestrian area. The exhaust fan as installed had an inline duct silencer but this was insufficient in terms of providing the desired noise mitigation. The project desire was not to make changes to the fan or its inline silencer or the external louvers so an alternative noise mitigation option had to be explored. Based on the provided sound power characteristics of the fan, the exterior noise levels as calculated matched the expected levels coming out of the metal louvers. The interior of the ventilation shaft is bare concrete with the fan installed though a hole in the concrete top floor. The predominate noise was the very high reverberation inside the ventilation shaft. The owner of the property made an attempt at installing noise absorption but this was not sufficient. Based on the field data the sound levels with the preliminary absorption solution matched expectation, but further noise reduction was required. A complete sound absorption on the walls of the concrete ventilation shaft noise mitigation solution was design, and the expected levels predicted to show that significant noise reductions can be obtained by a comprehensive noise absorption solution. The noise mitigation solution was implemented and exterior sound level measurements performed at the completion of the project. The measured sound levels outside of the metal louvers were in very good agreement with the predicted levels. Based on the success of this first noise mitigation solution, noise mitigation for a second ventilation system is not being considered.

Deep learning-based stereophonic acoustic echo suppression without decorrelation.

Traditional stereophonic acoustic echo cancellation algorithms need to estimate acoustic echo paths from stereo loudspeakers to a microphone, which often suffers from the nonuniqueness problem caused by a high correlation between the two far-end signals of these stereo loudspeakers. Many decorrelation methods have already been proposed to mitigate this problem. However, these methods may reduce the audio quality and/or stereophonic spatial perception. This paper proposes to use a convolutional recurrent network (CRN) to suppress the stereophonic echo components by estimating a nonlinear gain, which is then multiplied by the complex spectrum of the microphone signal to obtain the estimated near-end speech without a decorrelation procedure. The CRN includes an encoder-decoder module and two-layer gated recurrent network module, which can take advantage of the feature extraction capability of the convolutional neural networks and temporal modeling capability of recurrent neural networks simultaneously. The magnitude spectra of the two far-end signals are used as input features directly without any decorrelation preprocessing and, thus, both the audio quality and stereophonic spatial perception can be maintained. The experimental results in both the simulated and real acoustic environments show that the proposed algorithm outperforms traditional algorithms such as the normalized least-mean square and Wiener algorithms, especially in situations of low signal-to-echo ratio and high reverberation time RT60.

Field measurement of reverberation time and average absorption of one high-rise building room by road traffic noise penetrating facade

The facade insulation (FI) is one choice for Road traffic noise (RTN) at a high-rise accommodation building nearby a motor road. The weakness of FI is from window, so the window insulation (WI) is also a prioritized descriptor. ISO16283-3 states a field method to measure FI using RTN. However, in room acoustics, besides FI, reverberation time (RBT) or indoor average sound absorption (IASB) are another two un-ignorable descriptors. When the value of IASB is small, the indoor noise is not only contributed from penetrating façade RTN, but also supplemented by the residual sound from high reverberation field, weakening FI. As a parallel to ISO16283-3, this paper suggests an engineering method to measure RBT and IASB of one high-rise building room close to a motor road by penetrating façade RTN. It can supply a convenient tool for the field measurement of RBT and IASB with RTN. At the end, we made a field measurement of RBT, IASB, and WI at a hotel room nearby a viaduct in Hangzhou of China, assistant to adjust RBT or IASB and WI so as to improve the sound quality of the hotel. Further, the method can extend to the lines of rail, aviation, and shipping.

Effect of reverberation and noise type on speech intelligibility in real complex acoustic scenarios

Enhanced speech intelligibility in realistic acoustic scenarios guarantees effective communication. Noise and reverberation degrade speech intelligibility, but the combined effect of reverberation, informational noise and position of target, listener and noise source on speech intelligibility still needs to insights. This work investigates the effect of real complex acoustic scenarios on speech intelligibility for adults. In two primary-school classrooms with reverberation time of 0.4 s and 3.1 s, receivers were located on axis with the target at increasing distances, and noise sources were both co-located and spatially separated from the target at different distances providing various degrees of energetic and informational masking. Noise level was maintained constant and set at 60 dB at the receiver's position, regardless of the noise source distance. The longer reverberation time resulted in worse speech recognition thresholds (SRT80s) by 6 dB on average. The competitive effect of informational noise resulted in increased SRT80s by 7 dB on average, in comparison to energetic noise. The SRT80 increases by ~2 dB with doubling the target-to-receiver distance when the noise source is close to the receiver, accounting for both reverberations and noise types. The spatial release from masking resulted in improved speech intelligibility by up to ~3 dB when the noise source is 1 m far from the receiver for energetic masker for low reverberation and, unexpectedly, for the informational masker in high reverberation. This may indicate that a perceptual segregation mechanism sorts out competing voices of informational masker according to their directions in least favorable listening situations.

A RobustICA-based algorithmic system for blind separation of convolutive mixtures

In this paper, we propose a frequency-domain method employing robust independent component analysis (RICA) to address the multichannel Blind Source Separation (BSS) problem of convolutive speech mixtures in highly reverberant environments. We impose regularization processes to tackle the ill-conditioning problem of the covariance matrix and to mitigate the performance degradation. We evaluate the impact of several parameters on the performance of separation, e.g., windowing type and overlapping ratio of the frequency domain method. We then assess and compare different techniques to solve the frequency-domain permutation ambiguity. Furthermore, we develop an algorithm to separate the source signals in adverse conditions, i.e. high reverberation conditions when short observation signals are available. Finally, through extensive simulations and real-world experiments, we evaluate and demonstrate the superiority of the presented convolutive algorithmic system in comparison to other BSS algorithms, including recursive regularized ICA (RR-ICA) and independent vector analysis (IVA).