Reverberation Algorithms

The reverberation algorithm can be based on efficient infinite impulse response (HR) filters. 

The reverberation algorithm will provide real-time control of all the perceptually relevant parameters. The parameters do not need to be correlated as they often are in real rooms. 

In this paper, we will concentrate on the perceptually motivated method, because the resulting recursive algorithms are more practical and useful. We first present a concise physical and perceptual background for our study of reverberation, then discuss algorithms to simulate early reverberation, and conclude with a discussion of late reverberation algorithms. 

There are many possible reverberation algorithms that can be constructed by adding absorptive losses to allpass feedback loops, and these reverberators can sound very good. However, the design of these reverberators has to date been entirely empirical. There is no way to specify in advance a particular reverberation time function A(co), nor is there a deterministic method for choosing the filter parameters to eliminate tonal coloration. 

We will speak of a reverberation algorithm, or more simply, a reverberator, as a linear discrete-time system that simulates the input-output behavior of a real or imagined room. The problem of designing a reverberator can be approached from a physical or perceptual point of view. 

The first artificial reverberators based on discrete-time signal processing were constructed by Schroeder in the early 1960 s [Schroeder, 1962], and most of the important ideas about reverberation algorithms can be traced to his original papers. Schroeder s original proposal was based on comb and allpass filters. The comb filter is shown in figure 3.12 and consists of a delay whose output is recirculated to the input. The z transform of the comb filter is given by ... 

Two important criteria for the realism of a reverberation algorithm are the modal density and the echo density. The modal density of the parallel combs, expressed as the number of modes per Hz, is [Jot and Chaigne, 1991] ... 

All reverberation algorithms are susceptible to one or more of these faults, which usually do not occur in real rooms, certainly not good sounding ones. In addition to these criticisms, there is the additional problem that Schroeder s original proposal does not provide a frequency dependent reverberation time. 

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