### 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.

**Next Section:**

Perceptual Metrics for Ideal Reverberation

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Possibility of a Physical Reverb Model