Perceptual Aspects of Reverberation
Artificial reverberation is an unusually interesting signal processing problem because, as discussed in the previous sections, the ``obvious'' methods based on physical modeling or input-output modeling are too expensive computationally for most applications. This leads to the question of what are the perceptually important aspects of reverberation, and how can these be provided by efficient computational structures.Perception of Echo Density and Mode Density
The reverberation problem can be greatly simplified without sacrificing perceptual quality. For example, it can be shown^{4.3}that for typical rooms, the echo density increases as , where is time. Therefore, beyond some time, the echo density is so great that it can be modeled as some uniformly sampled stochastic process without loss of perceptual fidelity. In particular, there is no need to explicitly compute multiple echoes per sample of sound. For smoothly decaying late reverb (the desired kind), an appropriate random process sampled at the audio sampling rate will sound equivalent perceptually. Similarly, it can be shown^{4.4}that the number of resonant modes in any given frequency band increases as frequency squared, so that above some frequency, the modes are so dense that they are perceptually equivalent to a random frequency response generated according to some statistics. In particular, there is no need to explicitly implement resonances so densely packed that the ear cannot hear them all. In summary, we see that, based on limits of perception, the impulse response of a reverberant room can be divided into two segments. The first segment, called the early reflections, consists of the relatively sparse first echoes in the impulse response. The remainder, called the late reverberation, is so densely populated with echoes that it is best to characterize the response statistically in some way. Section 3.3 discusses methods for simulating early reflections in the reverberation impulse response. Similarly, the frequency response of a reverberant room can be divided into two segments. The low-frequency interval consists of a relatively sparse distribution of resonant modes, while at higher frequencies the modes are packed so densely that they are best characterized statistically as a random frequency response with certain (regular) statistical properties. Section 3.4 describes methods for synthesizing hiqh quality late reverberation.Perceptual Metrics for Ideal Reverberation
Some desirable controls for an artificial reverberator include [218]- desired reverberation time at each frequency
- signal power gain at each frequency
- ``clarity'' = ratio of impulse-response energy in early reflections to that in the late reverb
- interaural correlation coefficient at left and right ears
Energy Decay Curve
For measuring and defining reverberation time , Schroeder introduced the so-called energy decay curve (EDC) which is the tail integral of the squared impulse response at time :Energy Decay Relief
The energy decay relief (EDR) is a time-frequency distribution which generalizes the EDC to multiple frequency bands [215]:Next Section:
Early Reflections
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The Reverberation Problem