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Automated estimation of the truncation of room impulse response by applying a nonlinear decay model
Abstract
Noise represents one of the most significant disturbances in measured room impulse responses (RIRs), and it has a potentially large impact on evaluation of the decay parameters. In order to reduce noise effects, various methods have been applied, including truncation of an RIR. In this paper, a procedure for the response truncation based on a model of RIR (nonlinear decay model) is presented. The model is represented by an exponential decay plus stationary noise. Unknown parameters of the model are calculated by an optimization that minimizes the difference between the curve generated by the model and the target one of the response to be truncated. Different curves can be applied in the optimization—absolute value of the RIR, logarithmic decay curve, and Schroeder curve obtained by the backward integration of the RIR. The proposed procedure is tested on various synthesized and measured impulse responses. It is compared with the procedure taken from the literature, often applied in practice.
... However, the ambient and equipment noise is always present in environments, occurring in the room impulse response (RIR) during measurements [7]. The noise may lead to a characteristic curvature in the EDC [8,9]. Therefore, the dynamic range of the EDC is insufficient for the reliable determination of RT. ...
... According to the research [16], the TT can be manually determined by a simple method of an intersection of the main decay slope and the noise floor level. However, the non-exponential decay and the characteristic curvature in the EDC make the decay slope dependent on the ER [8,15], as seen in the decay slope (black dotted curve) in Figure 1. Observing Figure 1a, when the measured RIR has high initial peaks, the corresponding EDC presents a non-exponential decay behavior. ...
... In order to counteract the noise estimation influence in TT detection, techniques based on the energy-time curve analysis of the signal envelope are proposed since the noise level can be found and explicitly estimated [17,18]. A nonlinear decay model that consists of an exponential decay plus noise is fitted to energy-time functions of the measured RIR by applying the least-squares (LS) optimization to automatedly determine the TT [8,19]. Nevertheless, the model still leaves some uncertainty in the measured RIR with non-exponential decay. ...
The noise effects in the room impulse response (RIR) make the decay range of the integrated impulse response insufficient for reliable determination of reverberation time (RT). One of the preferred techniques to minimize noise effects is based on noise subtraction, RIR truncation, and correction for the truncation. The success of RT estimation through the method depends critically on the accurate estimation of the truncation time (TT). However, noise fluctuation and RIR irregularities can lead to discrepancies in the determined TT from the optimal value. The general goal of this paper is to improve RT estimates. An iterative procedure based on a non-exponential decay model consisting of a double-slope decay term and a noise term is presented to estimate the TT accurately. The model parameters are generated until the iterative procedure converges to a minimum difference between the energy decay curve (EDC) generated by the model and the Schroeder decay function. The decay rates of the EDCs with added pink noise levels are compared to those of the EDCs with low background noise. In addition, the detected TTs and the corresponding RTs are compared with the existing method and the noise compensation method (subtraction–truncation–correction method).
... Reverberation time (RT) is the most representative and physically important parameter related to the average properties of a room [1][2][3] and is essential for predicting speech intelligibility [4,5]. A well-known and widely used method to calculate RT is determined by the energy decay curve (EDC) generated by Schroeder's method [6]; however, the measured room impulse response (RIR) presents ambient noise, and equipment noise may deteriorate the EDC, leading to errors in predicting room acoustic parameters [7,8]. The relative errors for RTs, early decay time (EDT), and other acoustic parameters, without noise compensation, could exceed 5% [9,10]. ...
... For mathematical advantages, nonlinear regression methods [15] were investigated to fit the RIR to calculate the slope of the EDC. The technique was further developed as an automated detection method for calculating the correction term and determining the truncation time [5,8]. All the methods were set out from the time domain. ...
The generalized spectral subtraction algorithm (GBSS), which has extraordinary ability in background noise reduction, is historically one of the first approaches used for speech enhancement and dereverberation. However, the algorithm has not been applied to de-noise the room impulse response (RIR) to extend the reverberation decay range. The application of the GBSS algorithm in this study is stated as an optimization problem, that is, subtracting the noise level from the RIR while maintaining the signal quality. The optimization process conducted in the measurements of the RIRs with artificial noise and natural ambient noise aims to determine the optimal sets of factors to achieve the best noise reduction results regarding the largest dynamic range improvement. The optimal factors are set variables determined by the estimated SNRs of the RIRs filtered in the octave band. The acoustic parameters, the reverberation time (RT), and early decay time (EDT), and the dynamic range improvement of the energy decay curve were used as control measures and evaluation criteria to ensure the reliability of the algorithm. The de-noising results were compared with noise compensation methods. With the achieved optimal factors, the GBSS contributes to a significant effect in terms of dynamic range improvement and decreases the estimation errors in the RTs caused by noise levels.
... In a next step, the investigation of Lundeby et al. (1995) picks up a discussion voiced earlier by Barron (1984) and studies how reverberation times can be calculated while ensuring the background noise does not disturb the analysis. Lundeby et al.'s algorithm has attracted some recent attention (Guski & Vorländer, 2015;Jankovic, Ciric, & Pantic, 2016) where it is discussed that different strategies suffice with ISO 3382-1 (2009) but inhere different potential of error and uncertainty. Through this discussion, it becomes clear how a loose definition of the measurement and analysis specification can contribute to measurement uncertainty. ...
Regardless of the field, measurements are essential for validating theories and making well-founded decisions. A criterion for the validity and comparability of measured values is their uncertainty. Still, in room acoustical measurements, the application of established rules to interpret uncertainties in measurement is not yet widespread. This raises the question of the validity and interpretability of room acoustical measurements.
This work discusses the uncertainties in measuring room acoustical single-number quantities that complies with the framework of the ``Guide to the Expression of Uncertainty in Measurement''(GUM). Starting point is a structured search of variables that potentially influence the measurement of room impulse responses. In a second step, this uncertainty is propagated through the algorithm that determines single-number quantities.
A second emphasis is placed on the investigation of spatial fluctuations of the sound field in auditoria. The spatial variance of the sound field in combination with an uncertain measurement position marks a major contribution to the overall measurement uncertainty. To reach general conclusions, the relation between changes in the measurement location and the corresponding changes in measured room acoustical quantities is investigated empirically in extensive measurement series.
This study shows how precisely a measurement position must be defined to ensure a given uncertainty of room acoustical single-number quantities. The presented methods form a foundation that can be exibly extended in future investigations to include additional influences on the measurement uncertainty.
The use of voice control of unmanned aerial vehicles is relevant due to the ease of practical use and new opportunities. This technology allows one to simplify the interface, making it more intuitive and natural. However, the quality and intelligibility of speech signals indoors can be significantly impaired by noise and reverberation. Therefore, before using voice technologies, it is desirable to take into account the effect of interferences by preliminary assessment of their parameters. In this paper, an algorithm for estimating the boundary (truncation time) between the informative and non-informative parts of the room impulse response, which allows obtaining believable estimates of the reverberation time, is proposed. The proposed algorithm is two-stage. At the first stage, "rough" envelope of the room impulse response is calculated using the detector-integrator, which allows one to find an approximate value of truncation time and construct an approximate envelope of room impulse response using backward integration method to obtain an approximate estimate of the reverberation time. In the second stage, output data of the first stage are used to refine the truncation time and reverberation time estimates. Experimental tests using recordings of real room impulse responses testify to the efficiency of the proposed algorithm.
Serious effects of noise present in room impulse responses (RIRs) on evaluation of room acoustical parameters can be compensated by applying different methods. One of the preferred methods is based on the noise subtraction, RIR truncation and correction for truncation. This paper presents a procedure for calculation of the correction term that should be added to the backward integrated truncated RIR. The procedure can be applied in an automated way, and it is based on a nonlinear decay model consisting of an exponential decay plus stationary noise. Unknown parameters of the model are calculated by an optimization procedure where the model is fitted to the measurements. The proposed procedure for correction term calculation is tested on both synthesized and measured RIRs. The effects of the procedure parameters related to the RIR estimation range used for fitting the model to the measurements are analyzed. This procedure is compared with the one often applied in practice as a reference. The comparison shows that the proposed procedure outperforms the reference one. In addition, the impact of changing the correction term on the reverberation time estimation is investigated.
This paper presents the application and a method that calculates the reverberation time based on Lp-norms. generalized measures of the room impulse response (RIR). without using regression on decay curves. The reverberation time in this approach is a function of a parameter, and is constant only in a perfectly diffuse space; therefore the method may present useful information beyond the decay time itself. Properties of this method using theoretical and real-life RIRs are examined in cases of wide-band and sub-octave-band calculations. Correction methods for the finite support of the R IR . as well as for the effects of stationary background noise are presented and the connection to previous methods is shown.
Early-to-late energy ratios are used to predict speech intelligibility. The computation is based on the measured impulse response for a source-microphone combination. When measurement is corrupted by extraneous noise, the upper limit of integration cannot be the total time of acquisition, but a new time limit value defined as the useful length of the impulse response. This limit is validated with the reverberation time computed from the Schroeder backward integral. Results are shown for three highly reverberant rooms.
The evaluation of room acoustics characteristics has been thoroughly described in several papers since 60-ies. Moreover, the ISO 3382 standard describes several acoustic parameters and their measurements. However, there is only a few information about the methods of preprocessing the impulse responses (background noise compensation) that are required before calculating those parameters. In this paper the main processing methods (based on Chu, Lundeby and Hirata) are analyzed. Moreover they are compared with the results obtained without any processing (original Schroeder backward integration). In a further step, these methods are applied in some acoustic measurements of some opera houses in Italy. Finally some acoustic parameters are compared with the JND that is actually accepted in the evaluation of the mono-aural, binaural and spatial acoustic parameters.
Standards for measuring room acoustic parameters, such as ISO 3382, in many cases do not, or only partially, specify the requirements that a measured impulse response should meet to allow calculation of a certain parameter. Among other things, it is often left to the user of the standard to find a practical interpretation of the time infinity that appears in the theoretical formulas defining the parameters. Hence, the parameter value may depend on the decay range and measurement time. Under the most adverse conditions this may lead to variations in the calculated parameter values larger than the Just Noticeable Difference (JND). Using the suggested ISO 3382 'infinite' integration time limits for some parameters and otherwise the crosspoint of decay line and noise level as the 'infinite' integration time limit for the other parameters, the influence of the decay range on the calculated parameter values is investigated. This is done for all ISO 3382-1 parameters: EDT, T 20, T 30, C 80, D 50, TS, G, ST, IACC, LF, LFC and LG, using the INR (room Impulse response to Noise Ratio) as an estimator for the decay range. The result is a proposal for a minimum decay range value for all ISO 3382-1 parameters, based on the JND and the INR.
The evaluation of room acoustics characteristics in rooms has been thoroughly described in several papers since 1960s. Moreover, the ISO 3382 standard describes several acoustic parameters and their measurements. However, there are only a few information about the methods of pre-processing the impulse responses that are required before calculating those acoustic parameters. In this paper, the main processing methods (based on Luneby, Chu, and Hirata methods) are analyzed. Moreover, they are compared with the Schroeder (background integrated) methods. In a further step, these methods are applied in some acoustic measurements employed in some opera houses in Italy. Finally, after a full discussion about the uncertainties that is beyond these methods, the acoustic parameters are compared with the JND that is actually accepted in the evaluation of the mono-aural, binaural, and spatial acoustic parameters.
A method is proposed that provides an approximation of the acoustic energy decay (energy-time curve) in room impulse responses generated using the image-source technique. A geometrical analysis of the image-source principle leads to a closed-form expression describing the energy decay curve, with the resulting formula being valid for a uniform as well as nonuniform definition of the enclosure's six absorption coefficients. The accuracy of the proposed approximation is demonstrated on the basis of impulse-response simulations involving various room sizes and reverberation levels, with uniform and nonuniform sound absorption coefficients. An application example for the proposed method is illustrated by considering the task of predicting an enclosure's reflection coefficients in order to achieve a specific reverberation level. The technique presented in this work enables designers to undertake a preliminary analysis of a simulated reverberant environment without the need for time-consuming image-method simulations.
The room acoustical parameters, reverberation time RT, early decay time EDT, clarity factor C80, bass ratio BR, strength G, interaural cross-correlation coefficient IACC, and initial-time-delay gap ITDG [definitions in Hidaka et al., J. Acoust. Soc. Am. 107, 340-354 (2000) and Beranek, Concert and Opera Halls: How They Sound (Acoustical Society of America, New York, 1996)], were measured in 23 major opera houses under unoccupied conditions in 11 countries: Argentina, Austria, Czech, France, England, Germany, Hungary, Italy, Japan, The Netherlands, and the USA. Questionnaires containing rating scales on the acoustical quality of 24 opera houses were mailed to 67 conductors, 22 of whom responded. The objective measurements were analyzed for reliability and orthogonality, and were related to the subjective responses. Presented are (a) the rankings of 21 opera houses each rated by at least 6 conductors for acoustical quality as heard by them both in the audience areas and in the pit; (b) relations between objective room acoustical parameters and subjective ratings; (c) findings of the most important of the parameters for determining acoustical quality: RT (or EDT), G(M), ITDG, [1 - IACC(E3)], texture (appearance of reflectrograms in the first 80-100 ms after arrival of the direct sound), a lower limiting value for BR, and major concern for diffusion and avoidance of destructive characteristics (noise, vibration, echoes, focusing, etc.); (d) the differences between average audience levels with and without enclosed stage sets; and (e) the differences between average levels in audience areas for sounds from the stage and from the pit.
The estimation of modal decay parameters from noisy measurements of reverberant and resonating systems is a common problem in audio and acoustics, such as in room and concert hall measurements or musical instrument modeling. Reliable methods to estimate the initial response level, decay rate, and noise floor level from noisy measurement data are studied and compared. A new method, based on the nonlinear optimization of a model for exponential decay plus stationary noise floor, is presented. A comparison with traditional decay parameter estimation techniques using simulated measurement data shows that the proposed method outperforms in accuracy and robustness, especially in extreme SNR conditions. Three cases of practical applications of the method are demonstrated.
Several methods for measuring reverberation time in rooms have been compared to check the repeatability limits of interrupted noise methods and of methods using the integrated impulse response, and to determine the requirements for the methods to be set in the international measurement standards. Generally, all methods are state-of-the art and qualified for standardization. The restrictions on the use of integrated impulse methods include guidelines for the temporal limitation of the impulse response depending on the evaluation range of the decay curve. A simple rule relates the required length of the impulse response to the lower limit of the regression slope of the decay curve. The interrupted noise methods should preferably be based on ensemble averaging. Formula for estimating the measurement uncertainty of ensemble-averaged interrupted random noise decay curves are given. The time and effort to be spent, and hence the cost of the measurements, are comparable in the case of broad-band interrupted noise measurements and methods using band-limited impulses. The most powerful impulse method is the one using broad-band pseudorandom sequences with subsequent Hadamard transformation, digital filtering and reverse-tune integration. When this method and phase-locked averaging are applied, even signals below the background noise level can be used for reverberation time measurement.Zusammenfassung Es wurden mehrere Verfahren zur Messung der Nachhallzeit in Raumen verglichen, um die Wiederholbarkeit von Methoden mit abgeschaltetem Rauschen bzw. von Methoden mit integrierter Impulsantwort zu ermitteln und um Vorschläge für die erforderlichen Spezifikationen der Meßverfahren in internationalen Meßnormen machen zu können. Im großen und ganzen sind alle Meßverfahren Stand der Technik und zur Normung geeignet. Die Einschränkungen für den Einsatz der integrierten Impulsantwort beinhalten Leitlinien für die zeitliche Begrenzung der Impulsantwort, abhängig vom Auswertebereich der Nachhallkurve. Eine einfache Regel stellt den Zusammenhang her zwischen der benötigten Länge der Impulsantwort und dem unteren Stützwert der Anpassung einer Geraden an die Nachhallkurve. Die Nachhallkurven aus abgeschaltetem Rauschen sollten vorzugsweise über eine Scharmittelung gewonnen werden. Es werden Formeln zur Abschätzung der Meßunsicherheit in Abhängigkeit von der Anzahl der Scharmittel angegeben. Der Meßaufwand und damit die Kosten der Messung sind vergleichbar bei Verwendung von breitbandigen Rauschsignalen und von bandbegrenzten Impulsen. Die leistungsfähigste Impulsmethode ist diejenige mit breitbandigen Maximalfolgen, nachgeschalteter Hadamard-Transformation, digitaler Filterung und integrierter Impulsantwort. Mit dieser Methode und phasenstarrer Mittelung können sogar Signale mit einem Pegel unterhalb des Hintergrundgeräusches zur Nachhallzeitmessung benutzt werden.Sommaire Nous avons comparé plusieurs méthodes de mesure de la durée de réverbération dans les salles, pour vérifier les limites de reproducibilité des méthodes utilisant un bruit interrompu et celles basées sur la réponse impulsionnelle intégrée, et pour définir les conditions requises pour que ces méthodes puissent être intégrées aux normes internationales de mesures. D'une façon générate, toutes les méthodes sont bien au point et pourraient accéder à la normalisation. Il y a une réserve pour les méthodes à réponse impulsionnelle qui devraient inclure des indications sur les limites temporelles de la réponse, selon l'intervalle d' évaluation sur la courbe de décroissance. Une simple règie relie la longueur requise de la réponse impulsionnelle à la limite inférieure de la pente de régression de la courbe de décroissance. Les méthodes à bruit intermittent devraient plutôt être basées sur une moyenne d'ensemble. On fournit des formules permettant d'évaluer l'incertitude de la mesure déduite de cette méthode de moyenne. La durée et la difficulté de mise en oeuvre des mesures, et par conséquent leur coût, sont équivalentes pour les mesures faites à l'aide de bruit interrompu a large spectre et pour les méthodes utilisant des impulsions à spectre limité. La méthode impulsionnelle la plus puissante est celle qui utilize des séquences pseudo-aléatoires à large bande puis une transformation d'Hadamard, un filtrage numérique et une intégration inverse. En utilisant cette méthode avec une moyenne à verrouillage de phase, on arrive à utiliser des signaux de niveau même inférieur au bruit de fond pour la mesure de la durée de réverbération.
Noise that is part of the measured impulse responses is inevitable but can have a large impact on the evaluation of room acoustic parameters. Five well-known and widely used noise compensation methods are discussed and their performances are compared in this study. Two evaluation approaches
are used to test the different methods: A simple parametric model to simulate the envelope of an impulse response including measurement noise, and in a second approach, special designed long-term measurements. These were conducted to be able to evaluate the errors as a function of the noise
level. The results that are obtained using the model and the measurement approach are consistent with each other. When these methods are used to suppress noise effects, their performances differ significantly. This is also true for the three methods that are compliant with ISO 3382. Four methods
cause systematic errors depending on the peak-signal to noise ratio. The reverberation time is more sensitive to noise than energy parameters such as clarity or definition. A comparison of the different excitation signals that are used for the measurement approach shows that there is no difference
with regard to sine sweeps and maximum length sequences, if no impulsive noise or nonlinearities occur.
A theoretically obtained optimal Truncation Point (TP) in the Room Impulse Response (RIR) is located at the intersection of the main decay slope and the noise floor. Precise determination of this point is difficult in practice. Namely, the deviation of the RIR decay from the exponential decay can lead to discrepancies in the determined TP from the optimal value. In order to increase the accuracy of TP determination, additional terms are incorporated in a simple algorithm. Besides, iterative algorithm for RIR truncation is proposed. These are compared with the existing one, using simulated and measured RIRs. The results confirm the validity of the proposed algorithms, indicating their advantages. In addition, the influences of the response parameters on RIR truncation are investigated.
Backward integration of a room impulse response has long been used in room acoustics for the estimation of reverberation time. However, the inevitable noise floor limits the minimum level of the measured impulse response, thereby leading to errors. This paper shows how the error is influenced by the selection of truncation time and evaluation range. A general guideline that emerges from this study is to truncate the measured impulse response at the knee where the main decay slope intersects the noise floor, then measure the slope of the backward integrated truncated impulse response down to a level about 5 dB above the noise floor. (C) 1997 Acoustical Society of America.
The influence of several sources of error on room acoustical measurements have been investigated using maximum-length sequences (MLS). The algorithms for the determination of room acoustical parameters used by different analyzers introduce systematic differences caused by differences in time windowing and filtering, in reverse-time integration and in noise compensation. The overall uncertainty of measurements is of the same magnitude or a little higher than subjectively perceivable changes in room acoustical parameters when the measurements are performed according to ISO/DIS 3382. However, the draft standard allows various procedures to be applied in the processing of impulse responses.
Reverberation decay curves can be obtained by the backward integration
of room impulse responses proposed by M. R. Schroeder. The evaluation
of reverberation times is often achieved by a linear regression line
fitting the reverberation decay curves. However, under noisy conditions,
the successful application of this method requires either a careful
choice of the integration limit or a precise estimate of the mean-square
value of the background noise. In the present paper, an alternative
method using a nonlinear iterative regression approach for evaluating
reverberation times from Schroeder's decay curves is proposed. A
nonlinear model of the decay curves, established according to the
nature of Schroeder's decay curves, is used for the regression process
rather than the linear model used in linear regression. The regression
process is based on the generalized least-squares error principle
in which a rapid convergence can be observed. Preliminary experiments
show a slight dependence of the reverberation time T30dB on both
the integration limit and the background noise. Using this approach,
a high precision of reverberation time evaluations can be achieved
without either careful selection of the integration limit or precise
estimation of the mean square value of the background noise.
A new method of measuring reverberation time is described. The method
uses tone bursts (or filtered pistol shots) to excite the enclosure.
A simple integral over the tone-burst response of the enclosure yields,
in a single measurement, the ensemble average of the decay curves
that would be obtained with bandpass-filtered noise as an excitation
signal. The smooth decay curves resulting from the new method improve
the accuracy of reverberation-time measurements and facilitate the
detection of nonexponential decays.
Utilizing a digital acquisition system and minicomputer, two promising techniques for accurate determination of reverberation times have been studied in detail from the viewpoint of standard reverberation room tests. The first is Schroeder's "integrated impulse method," and special attention was given to the question of repeatability and the influence of signal-to-noise ratio on the successful application of the method. The second technique involves taking an ensemble average of a large number of logarithmic decay curves. It was found that, even for nonuniform decays, the average decay curves obtained by the second method compared well with those determined by the Integrated Impulse Method. A l'aide d'un réseau numérique de saisie des données et d'un mini-ordinateur, on a étudié à fond deux méthodes pour la détermination des périodes de réverbération du point de vue des essais effectués dans des salles de réverbération. La première méthode est la "méthode d'impulsions intégrées" de Schroeder; on a prêté une attention particulière au caractère répétitif et à l'influence du rapport signal-bruit sur le succès de la mise en application de la méthode. La deuxième méthode inclut le calcul de la moyenne d'un grand nombre de courbes de décomposition logarithmiques. On a remarqué que, même dans le cas de décompositions non uniformes, les courbes moyennes de décomposition obtenues selon la deuxième méthode correspondent de près aux courbes obtenues par la méthode d'impulsions intégrées. RES
This paper reviews a statistical time-frequency model of late reverberation decays, and describes an associated analysis procedure for deriving the time-frequency envelope of the reverberation from a measured impulse response, based on the notion of "Energy Decay Relief". The models and techniques discussed are applied to the representation of room acoustical quality, the characterization and equalization of transducers in diffuse fields, the restoration (denoising) of measured room impulse responses, as well as artificial reverberation and distance effects in virtual auditory displays and audio mixing systems. - 0 Introduction A stochastic model of room responses was proposed by Schroeder in the 1950s and further developed more recently by Polack [1-3]. This model is reviewed in the first section of this paper and applies to late diffuse reverberation decays, which will be the main concern of this paper. Statistical models bear a particular importance for auralization and syntheti...
The ISO 3382 parameters: Can we simulate them? Can we measure them? Google Scholar
- C L Christensen
- G Koutsouris