A guide for the

*sum* of the

delay-line lengths is the desired

*mode density*. The sum of

delay-line lengths

in a lossless

FDN is simply the

*order* of the system

:

The order increases slightly when lowpass

filters are introduced after
the delay lines to achieve a specific

reverberation time at low and
high frequencies (as described in the next subsection).
Since the order of a system equals the number of

poles, we have that

is the number of poles on the unit circle in the lossless
prototype. If the modes were uniformly distributed, the mode density
would be

modes per Hz. Schroeder [

417]
suggests that, for a

reverberation time of 1 second, a mode density of
0.15 modes per Hz is adequate. Since the mode widths are inversely
proportional to reverberation time, the mode density for a
reverberation time of 2 seconds should be 0.3 modes per Hz, etc. In
summary, for a sufficient mode density in the

frequency domain,
Schroeder's formula is

For a

sampling rate of 50 kHz and a reverberation time (

)
equal to 1 second, we obtain

.

**Next Section:** Prime
Power Delay-Line Lengths**Previous Section:** Mean Free Path