The method for calculating reverberation time from impulse response was published by Schroeder in 1965. As I explained last time, with the advancement of digital signal processing technology and the widespread use of PCs for room acoustic measurement, this method was standardized in 1997, more than 30 years later.
This time, I will briefly explain the meaning of impulse response, its measurement method, and the process of calculating reverberation time from the impulse response integration method.
Impulse response is defined as "the output of a system when a very short signal called an impulse is input." Historically, measuring impulse response in a room such as a hall involved using the sound of a pistol firing at the start of a competition, making a "bang" sound on stage, and observing the decay process of the sound from the audience seats. A simpler method is to clap your hands, which also produces a short, pulse-like sound, giving an impression of the room's acoustics. In room acoustics, a very short signal input is the generation of a pulsed sound source into the room as described above, and the system's output is the response at the receiving point (sound pressure time waveform due to direct sound and reflected sound). This impulse response contains all the physical acoustic information regarding the relationship between a sound source and the receiving point, even though the direction of each individual reflected sound on the waveform is unknown (see Figure 1).
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Figure 1 Conceptual diagram of impulse response
Nowadays, measurements are taken using a speaker instead of a pistol, but since speakers typically have strong directivity, especially in the high-frequency range, it is common to use an omnidirectional dodecahedron speaker. There are three main methods for determining the type of signal used as the sound source.
- Pulse sound
This method involves radiating electrical signal pulses from a speaker, directly emitting the pulsed sound itself into space and recording it. While intuitive, the low energy of the pulses usually necessitates synchronous summing to improve the signal-to-noise ratio. - M-sequence noise
An M-sequence signal (maximum length sequence signal) is a white-type pseudo-random signal consisting of a binary sequence (-1 and 1) with a period of length 1 L = 2N − 1. By using a technique called the fast Hadamard transform, which efficiently calculates the cross-correlation function, the impulse response can be obtained very quickly. The signal-to-noise ratio can be sufficiently obtained by optimally setting the recording time, but it is important to note that it is susceptible to the effects of time variation in the sound field. - Sweep Pulse
A sweep signal is a signal with continuously changing frequency, making it useful when you want to measure the characteristics of an arbitrary frequency band at once. This method involves emitting a sweep pulse (time-extended signal) with higher energy than a normal pulse signal, and performing calculations (time compression) during recording. Because the energy is considerably higher than a normal pulse, a good signal-to-noise ratio (S/N) is also ensured. Another advantage of this method is that you can perceive the reverberation audibly during measurement.
Next, we will explain the process of determining the reverberation time from the impulse response measured using the method described above.
As mentioned at the beginning, Schroeder showed that the decay curve obtained by integrating the time data obtained by squaring the impulse response with the time axis reversed is theoretically identical to the decay curve obtained by removing the random noise, as shown previously.
The decay as a function of time can be expressed by equation (1).
However, p(t) represents the impulse response. The integral in equation (1) can also be divided into two integral operations as shown in equation (2).
The slope of the straight line is determined using the least squares method for the attenuation curve, as explained previously, for the attenuation curve obtained using the above formula. It is desirable to ensure a dynamic range of at least 20 dB, and preferably 30 dB. Furthermore, the dynamic range used in the measurement must be clearly stated.
In this method, if the signal-to-noise ratio is not sufficient, noise is superimposed on the original reverberation component in the later part of the impulse response duration, resulting in a problem where a large bend occurs in the later part of the decay curve in the direction of flatness.
The standard (ISO 3382-1:2009) outlines processing methods to minimize the effects of background noise, but these are not very practical. It is important to use a measurement system and method that can ensure a dynamic range of at least 20 dB. Various factors determine the dynamic range, including the background noise level of the sound field, the speaker output level, the choice of the three methods mentioned above, synchronization summation, and signal length. It is true that determining how much dynamic range can be ensured requires knowledge and a certain level of experience.
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○ ISO 3382-1：2009 Acoustics -- Measurement of room acoustic parameters
Part 1: Performance spaces
○ ISO 3382-2：2008 Acoustics -- Measurement of room acoustic parameters
Part 2: Reverberation time in ordinary rooms
○ M. R. Schroeder，"A new method of measuring reverberation time" J. Acoust. Soc. Am.，vol. 37，pp 409－412，1965
Ono Sokki DS-0232 Sound Insulation/Sound Absorption Characteristics Measurement Software
(Excerpt from the email newsletter issued on December 22, 2010)
