## 4 Normalization of Measurement Results  
### Normalization of the Impulse Response  
To facilitate the comparison of room acoustic measurements made under different atmospheric conditions, the results should be normalized to the same conditions of temperature and relative humidity. The ambient atmospheric pressure is assumed to be that of the International Standard Atmosphere at mean sea level, namely 101.325 kPa, the reference air temperature is 20 \({}^{\circ}\)C, and the reference relative humidity is 50% [20]. The accuracy of the measured temperature and relative humidity should be at least (\(\pm\)1 \({}^{\circ}\)C) and (\(\pm\)3% RH), respectively. To illustrate the amount of correction needed for normalization of the impulse response, Figure 6 shows as an example the air attenuation as a function of time of propagation for dry air (20 \({}^{\circ}\)C, 30% RH) and for the standard air condition (20 \({}^{\circ}\)C, 50% RH). The correction that is needed for normalization at a given octave band is the difference between the pair of curves. At 4 kHz, the correction exceeds 10 dB after 2 s.  
The approximation using linearization is not suited to normalizing the impulse response, because it will cause some visible jumps at the knee points. Therefore, the summation method is applied. The reverberation time and many other room acoustic parameters are derived from the integrated, squared impulse response (the decay curve). This is the relative sound pressure level as a function of time, where the time is relative to the arrival of the direct sound. However, every single contribution to the impulse response can be considered a function of the path length of a sound travelling from the source to the receiver along some reflection path. Then, the time axis can be replaced by a distance axis, and Equation (2) yields the relation between time \(t\) and distance \(r\). The distances of the sound paths start at the sound source. The arrival times of each reflection can be replaced by the total length of the reflection path. Due to this transfer from the time domain to the distance domain, the influence of the temperature-dependent speed of sound is eliminated. This principle holds for squared impulse response and the integrated squared impulse response (decay curve). The fact that the speed of sound changes with the air temperature means that the time scale of the impulse response is not the same at different temperatures. To overcome this problem, the measured squared impulse response (or the decay curve) is converted to the distance domain before performing the correction for air absorption. Thus, normalization is carried out in three steps. STEP 1: In each octave band, the measured squared impulse response is converted to the distance domain, where the distance \(r(t)\) is calculated from Equation (3) using the speed of sound \(c\) at the temperature during the measurement, calculated from Equation (4). Figure 6: Air attenuation in octave bands at 20 \({}^{\circ}\)C and two different relative humidities. Full lines: 30% RH. Dashed lines: 50% RH. STEP 2: Each sample of the impulse response is related to a distance \(r\) of sound propagation, and it is corrected by subtraction of the air attenuation during the measurements and addition of the air attenuation for the reference conditions, both in the distance \(r\). The octave-band attenuations are calculated using the summation method (Equation (5)). The correction that applies to the instantaneous octave-band sound pressure level of the squared impulse response in the distance \(r\) is calculated using Equation (10). \[\Delta L_{\text{B}}(r)=\delta L_{\text{B},\,0}(r)-\delta L_{\text{B}}(r) \tag{10}\]  
where  
\(\delta L_{\text{B}}(r)\) is the octave-band attenuation at the distance \(r\), Equation (7), at the temperature and humidity during the measurement, in decibels,  
\(\delta L_{\text{B},0}(r)\) is the octave-band attenuation at the distance \(r\), Equation (7), at the reference temperature and humidity, in decibels.