- Delay line lengths
typically
*mutually prime* - For
*sufficiently high mode density*, must be sufficiently large.- No ``ringing tones'' in the late impulse response
- No ``flutter''

**Mean Free Path**

where is the total volume of the room, and is total surface area enclosing the room.

Regarding each delay line as a mean-free-path delay, the mean free path length, in samples, is the average delay-line length:

where = sound speed and = sampling period.

This is only a lower bound because many reflections are
*diffuse* in real rooms, especially at high frequencies
(one plane-wave reflection scatters in many directions)

**Mode Density Requirement**

FDN order = sum of delay lengths:

- Order = number of poles
- All poles are on the unit circle in the lossless prototype
- If uniformly distributed, mode density =
- Schroeder suggests that 0.15 modes per Hz

(when second) - Generalizing:
- Example: For kHz and second,
- Note that is the length of the FIR filter giving an exact implementation. Thus, recursive filtering is about 7 times more efficient by this rule of thumb.

Download Reverb.pdf

Download Reverb_2up.pdf

Download Reverb_4up.pdf

REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .

Released

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University