Energy Decay Curves

The starting point for the calculation of most acoustic parameters is the EDC curve. An impulse response (IR), $h(t)$, is a response at a receiver to an impulse generated at a source position. This is equivalent to a sound evolution over time measured/registered at the receiver position, when there is a hand clap (ideally infinitesimally short) at the source position. By analyzing the IRs at sufficiently many locations, we can evaluate the global behavior of the room whether it is suitable for the intended purpose. A concert hall needs a certain reverberation for enjoying music, as too dry conditions are not pleasant both for musician and audience. A classroom with too much reverberation can make listeners suffer in understanding what is being said.

The accuracy of estimated reverberation times is largely limited by the random fluctuation in the decay curve, once we used the square of the impulse response, $h^2(t)$. These random fluctuations result from the mutual beating of normal modes of different natural frequencies. One way to minimize the effect of the fluctuations in decay curves is to repeat the reverberation measurements many times which is rather impractical. In 1965, Schroeder suggested a backward integration method that can yield a decay curve from a single measurement, which is identical to the average over infinitely many decay curves that would be obtained from exciting the enclosure with bandpass-filtered noise [1]. The energy decay curve is calculated as follows and generally presented in dB.

$$R(t) = \int_t^{\infty} h^2(\tau)\,d\tau$$

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References

[1] M. R. Schroeder. New method of measuring reverberation time, J. Acoust. Soc. Am., 37:409, 1965.