Energy Decay Relief
The
energy decay relief (EDR) is a timefrequency distribution
which generalizes the
EDC to multiple frequency bands [
215]:
where
denotes bin
of the
shorttime Fourier transform
(
STFT) at timeframe
[
12,
451], and
denotes the total number of time frames. The
FFT within the STFT is
typically used with a window, such as a
Hann window of length 30 or 40
ms.
Thus,
is the total amount of
signal energy remaining
in the reverberator's
impulse response at time
in a frequency band centered
about
Hz, where
denotes the FFT length.
The EDR of a violinbody
impulse response is shown in Fig.
3.2.
For better correspondence with audio perception, the frequency axis is
warped to the
Bark frequency scale [
459], and energy
is summed within each
Bark band (one
critical band of
hearing equals
one
Bark). A violin body can be regarded as a very small reverberant
room, with correspondingly ``magnified'' spectral structure relative
to reverberant rooms.
Figure 3.2:
Energy Decay Relief of a violinbody impulse response
(from [203]).

The EDR of the Boston Symphony Hall is displayed in [
153, p.
96].
The EDR is used to measure partial
overtone dampings from recordings
of a
vibrating string in §
6.11.5.
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