Perceptual Metrics for Ideal Reverberation
Some desirable controls for an artificial reverberator include [218]
-
desired reverberation time at each frequency
signal power gain at each frequency
``clarity'' = ratio of impulse-response energy in early reflections to that in the late reverb
interaural correlation coefficient at left and right ears
The time to decay 60 dB () is a classical objective parameter
used as a measure of perceived reverberation time. Classically,
was measured for the whole response. More recently
[216], it has become more common to design for a given
at more
than one frequency, e.g., one for low frequencies, another for high
frequencies, and interpolated values at intermediate frequencies.
Perceptual studies indicate that reverberation time should be
independently adjustable in at least three frequency bands
[217].
Energy Decay Curve
For measuring and defining reverberation time , Schroeder
introduced the so-called
energy decay curve (EDC) which is the tail integral of the squared impulse
response at time
:
![$\displaystyle \hbox{EDC}(t) \isdef \int_t^\infty h^2(\tau)d\tau
$](http://www.dsprelated.com/josimages_new/pasp/img686.png)
![$ \hbox{EDC}(t)$](http://www.dsprelated.com/josimages_new/pasp/img687.png)
![$ t$](http://www.dsprelated.com/josimages_new/pasp/img122.png)
![$ t_{60}$](http://www.dsprelated.com/josimages_new/pasp/img668.png)
Energy Decay Relief
The energy decay relief (EDR) is a time-frequency distribution which generalizes the EDC to multiple frequency bands [215]:
![$\displaystyle \hbox{EDR}(t_n,f_k) \isdef \sum_{m=n}^M \left\vert H(m,k)\right\vert^2
$](http://www.dsprelated.com/josimages_new/pasp/img688.png)
![$ H(m,k)$](http://www.dsprelated.com/josimages_new/pasp/img689.png)
![$ k$](http://www.dsprelated.com/josimages_new/pasp/img89.png)
![$ m$](http://www.dsprelated.com/josimages_new/pasp/img6.png)
![$ M$](http://www.dsprelated.com/josimages_new/pasp/img11.png)
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 violin-body 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.
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.
Next Section:
Desired Qualities in Late Reverberation
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Perception of Echo Density and Mode Density