of Microprocessors

DIGITAL FILTERING 509
Even with a perfect delay line, the string of equally spaced echos
produced is not at all like concert hall reverberation. In an empty concert hall
a clap of the hands produces not a series of echos but what sounds like white
noise with a smoothly decreasing amplitude. The amplitude decrease approximates
an inverse exponential function, which if plotted in decibels would be
a constant number of decibels per second. The rate of decrease is generally
specified by stating the time required for a 60-dB reduction in reverberation
amplitude. This figure is used because under normal circumstances the reverberation
has become inaudible at that point. Typical reverberation times
for concert halls are in the 1.5-sec to 3-sec range, although values from near
zero to somewhat more than this may be useful in electronic music.
Echo density is another parameter that can be used to characterize a
reverberation process in general terms. The single delay line teverberator
suffers from a low (and constant) echo density of 0.03 echos/msec. In a
concert hall, the echo density builds up so rapidly that no echos are perceived.
One measure of the quality of artificial reverberation is the time
between the initial signal and when the echo density teaches 1/msec. In a
good system, this should be on the order of 100 msec. Furthermore, there
should be a delay of 10 msec to 20 msec between the signal and the very first
echo if a sense of being far away from the sound is to be avoided. Finally, if
the reverberation amplitude decrease is not smooth, a somewhat different yet
distinct echo effect is perceived. A plot of the impulse response of the
reverberator is a good way to visualize the buildup of echos and the overall
smoothness of amplitude decrease.
A natural consequence of any reverberation process is an uneven
amplitude response. For example, if the amplitude response of the singleecho
generator described earlier were measured, it would be found to rise and
fall with a period (in frequency) equal to the reciprocal of the delay time. In
fact, examination of the signal flow reveals that it is the same as that of a
comb filter! However, since the ratio of delayed to direct signal is normally
less than unity, the notch depth is relatively shallow. The feedback delay line
has the same properties except that the feedback results in a series of resonances.
As the feedback factor approaches unity, the Qs of the resonances get
quite high, producing a very uneven amplitude response.
Concert hall reverberation also has an'uneven amplitude response, but
the peaks and valleys are closely spaced, irregular, and not excessively high or
deep. It is not unusual to find several peaks and valleys per hertz of bandwidth
with an average difference between peak and valley of 12 dB. It is possible to
have high echo density combined with a low resonance density. An excellent
example is an empty locker room at even a metal garbage can. The small size
of the reverberant chamber precludes resonant modes spanning a large
number ofwavelengths of moderate frequency sound. The converse situation,
a high resonance density but low echo density, can be produced by the
feedback delay line reverberator with a very long delay time, which does not
sound like reverberation at all.