#### Mode Density Requirement

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 .
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