Energy Decay Curve

Background:

The reverberant sound in an auditorium or cathedral dies away with time, as the acoustic energy is absorbed by multiple interactions with the surfaces of the room. In a sonically more reflective room, it will take longer for the sound to die away; such a room is said to be 'live'. In a very absorbent room, the sound will die away quickly, and the room will be described as being acoustically 'dead'.

But the time for reverberation to completely die away will depend upon how loud the sound was to begin with, and will also depend upon the acuity of the hearing of the observer. In order to provide a reproducible parameter, a standard reverberation time has been defined as the time for the sound to die away to a level 60 decibels below its original level. A decrease in 60 decibels, regardless of the initial loudness of the sound, corresponds to the acoustical energy dropping to one-millionth of its original sound pressure level.

The reverberation time can be modeled to permit an approximate calculation. Here is where the Energy Decay Curve comes in:

The Energy Decay Curve (also known as EDC, Schröder curve, or Schroeder curve) is used in room acoustics to determine the reverberation time. It is a curve obtained by backward integration of the energy of the room impulse response (RIR): the integration starts from the end of the finite length RIR using the following formula:

<math>EDC(t)=10{\log}_{10} edc(t) =10{{\log }_{10} \left({{\int^{\infty }_t{h^2(\tau )d\tau }}\over {\int^{\infty }_0{h^2(\tau )d\tau }}}\right)\ }=10{{\log }_{10} \left(1-{{\int^t_0{h^2(\tau )d\tau }}\over {\int^{\infty }_0{h^2(\tau )}d\tau }}\right)}</math>

The denominator in the formula above is the energy of the room impulse response so the EDC curve is normalized and therefore always starts from 0 dB. In a perfectly diffuse sound field the decay is exponential, so the EDC curve is a linear slope.

Main advantages

• a smooth curve
• decreases monotonically
• starts from 0 dB

Due care is required, however, to determine the reverberation time using the EDC, since the slope of the curve is affected by both the noise and the finite length of the room impulse response.