Measuring Room Impulse Responses: Impact of the Decay Range on Derived Room 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 param eter. 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 , T20, T30, C80, D50, 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. PACS no. 43.55.Br, 43.58.Gn, 43.60.Cg, 43.55.Mc #### 1. Introduction Many room acoustic parameters are derived from room impulse responses. Figure 1 shows an example of a mea sured impulse response and its derived Energy Time Curve (ETC). Examples of room acoustic parameters are the sound strength, which is related to the sound energy level, the reverberation time, which is related to the energy de cay rate and the clarity, definition and centre time, which are related to early to late energy ratios of the impulse re sponse. Standards for measuring these room acoustic parame ters, such as ISO 3382 [1, 2, 3], 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. For instance, to determine the reverber ation time, clear requirements are stated with regard to the exponential shape of the decay curve and the associated decay range, i.e. the T30 can only be calculated if the de cay range is at least 45 dB while for T20 the requirement is a decay range of at least 35 dB. To calculate the Sound Received 25 April 2012, accepted 2 September 2012. ∗ Renz van Luxemburg passed away on 12 February 2012 Strength (G) from an impulse response, ISO 3382 requires a minimum decay range of 30 dB, and sets the integration time limit to the point were the decay curve has decreased by at least 30 dB. For the Inter Aural Cross Correlation (IACC) an integration time limit in the order of the rever beration time is suggested, irrespective of the noise level. For the Support (ST ) the integration time limit for the late energy is set to 1 s. For all other room acoustic parameters no practical value is specified for the decay range and/or the late energy integration time limit. It is therefore often left to the user of the standard to findapractical interpre tation of the time infinity that appears in the theoretical formulas defining the parameters. Under the most adverse conditions this may lead to variations in the calculated pa rameter values much larger than the JND. To the knowl edge of the authors extended research on this topic has not yet been performed. In theory the room acoustic formulas hold for infinite measurement times and the absence of noise, while ob viously neither of these conditions can be met in prac tice. For IACC calculations, ISO 3382 suggests using the reverberation time as the integration limit. This may be valid as long as the decay range of the impulse response is sufficiently large, or has been increased artificially us ing a noise compensation technique. Otherwise a relatively large section of noise might be unintentionally included in © S. Hirzel Verlag · EAA 907 -100 -50 0 100 -40 -50 -30 -20 -10 0 h(t) dominant n(t) dominant Decay Range 0.5 1.0 1.5 0 1 0.5 .0 1.5 0 t [s] t [s] Figure 1. Measured impulse response p(t) and Energy Time Curve 10 lg p 2(t), where h(t) is the actual system response and n(t) is the noise. t c(ross) Decay Range -40 -50 -30 -20 -10 0 0 t [s] Figure 2. The crosspoint tc is defined as the point where the im pulse response decay line crosses the noise level and is used as the ‘infinite’ integration limit for calculating room acoustic pa rameters. the calculations, making the results dependent on the noise level. For IACC it has never been investigated whether the reverberation time as the integration limit is the optimum choice. For all other energy ratio parameters no interpreta tion of time infinity is given at all. For practical measurements of finite length, one might equate infinity with the end of the impulse response mea surement. However, in the presence of noise this results in parameter values that depend on the length of the mea surement and the decay range. It seems most obvious to include as much as possible of the decaying impulse re sponse while excluding most of the noise. Therefore, it is proposed to use the crosspoint of decay line and noise level (tc(ross)) as the ‘infinite’ integration limit as shown in Fig ure 2. However, this still suggests that the parameter value may depend on the available decay range, as tc depends on the decay range. To the knowledge of the authors it has never been investigated what decay range is necessary to sufficiently reduce the measurement uncertainty for the ISO 3382-1 parameters. In this paper, the influence of the decay range on all ISO 3382-1 parameters is investigated. Decay Range PNR Decay range Initial peak a b Figure 3. The Peak-to-Noise Ratio (PNR) fails to describe the decay range of a room acoustic Energy Time Curve (ETC). The upper graph (3a) shows the ETC of a theoretically diffuse sound field. The lower graph (3b) shows the effect of a high initial peak on the effective decay range. A description of the investigated parameters with the in tegration time limit interpretation is presented in Table I. In section 2, a definition of the decay range is given and a decay range estimator is proposed. In section 3 to 5, the error of calculated parameter values is investigated when reducing the decay range of a large set of practical impulse responses. #### 2. Decay range definition 2.1. Introduction The definition of the reverberation time presumes that the (backward integrated) RMS value of a room acoustic im pulse response follows a straight line when plotted on a dB scale. The reverberation time is then calculated from the slope of the regression line over the largest useful range of this plot. This regression range is directly related to the decay range, which in turn is limited due to measurement noise. The ISO 3382 standard [1] prescribes a minimum decay range of 35 dB for the measurement of T20 (regres sion range − 5 to − 25 dB) and of 45 dB for the measure ment of T30 (regression range − 5 to − 35 dB). The ISO 18233 [1