Late Reverberation

A good late reverberation should have a smooth decay and a smooth frequency response.

Some fluctuation in the short-term energy is needed to achieve a natural sound (Blesser, 2001; Dattorro, 1997).

Moorer's ideal late reverb: exponentially decaying white noise. But it would be better to say exponentially decaying “colored” noise, since the high-frequency energy should decay faster than the low-frequency energy.

Schroeder (1962) suggested the use of parallel comb filters and cascaded allpass filters to synthesize reverberation.

**Figure 9:** Cascaded Schroeder allpass sections.
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Allpass filters produce frequency-dependent time shifts, which help diffuse the sound. For this reason, Schroeder allpass sections are sometimes referred to as impulse expanders or impulse diffusers.

The gain values are typically set around $g = 0.7$

. The delay-line lengths $M_{i}$ should be mutually prime and span successive orders of magnitude.

**Figure 10:** Impulse response of three cascaded Schroeder allpass sections ( = 0.7 and $M_{i}$ = [113, 337, 1051]).
$\begin{figure}\begin{center} \epsfig{file = figures/allpass-response.eps,width=3.5in} \end{center} \end{figure}$

The impulse response, calculated with the Matlab script allpass.m, of three cascaded Schroeder allpass sections is shown in Fig. 10.

The feedback comb filters provide coloration and the delay-line lengths are set to mutually prime values.

**Figure 11:** The JCRev reverberator from CCRMA (based on Schroeder/Moorer).
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The STK classes PRCRev, JCRev, and NRev implement Schroeder reverberators of various complexities. In particular:

PRCRev implements two series allpass units and two parallel comb filters.
JCRev implements three series allpass units, four parallel comb filters, and two decorrelation delay lines in parallel at the output.
NRev implements six parallel comb filters, three series allpass units, a lowpass filter, another allpass filter in series, followed by two allpass filters in parallel at the output.