Desired Qualities in Late Reverberation

From a perceptual standpoint, the main qualities desired of a good late-reverberation impulse response are

1. a smooth (but not too smooth) decay, and
2. a smooth (but not too regular) frequency response.

Providing an exponential decay is no problem since both stable linear systems and natural reverberation decay exponentially. The harder issue is making it smooth, that is, free of ``flutter,'' ``beating,'' or other unnatural irregularities. In general, smooth decay results when the echo density is sufficiently high. Note, however, that some fluctuation in the short-term energy is needed to sound natural [58,102], corresponding to that of a decaying noise process [322].^3.6

A smooth frequency response exhibits no large, isolated gaps or boosts. It is generally provided when the mode density is sufficiently large in the frequency domain, with the modes being spread out uniformly, as opposed to piling up in the same place or separated to form gaps. On the other hand, the modes should not be too regularly spaced, since this can produce audible periodicity in the time-domain impulse response.

An interesting experiment by Moorer [322] was to try exponentially decaying white noise as a late reverberation impulse response. This signal satisfies both smoothness criteria (time domain and frequency domain), and it sounds quite natural. However, since natural reverberation decays faster at high frequencies, it is better to say that the ideal late reverberation impulse response is exponentially decaying ``colored'' noise, with the high-frequency energy decaying faster than the low-frequency energy.

Schroeder's rule of thumb for echo density in the late reverb is 1000 echoes per second or more [426]. However, for impulsive sounds, 10,000 echoes per second or more may be necessary for a smooth response [220,156].

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.