# Reverberation

Recursive Comb Filter (IIR):

When the delay D of an IIR comb filter is small, the effect is spectral. However when the delay is larger than 10 ms, it creates a series of decaying echoes. The time it takes for the output of the comb filter to decay by 60 dB is specified by:

decay_time = (60 / -loopGain) * loopDelay

loopGain is the gain g expressed in decibels loopDelay is the delay expressed in seconds

Allpass Comb Filter:

If an FIR Comb Filter and an IIR Comb Filter are used together, they don't change the individual amplitudes of frequency bands, but they do change the phase of the signal by coloring sharp transient signals.

When the delay time of the filter is long enough (between 5 and 100 ms), the allpass filter has an impulse response of a series of exponentially decaying echo pulses. The initial output is inverted in phase, and happens only once. The uniform spacing between the pulses suggests that when a transient sound is applied, the filter rings with a period equal to the delay time of the filter.

Because IIR and FIR comb filters are being used at the same time, their is no frequency activity.

## Manfred Schroeder Reverberation

Manfred Schroeder studied concert hall reverberation while working on his Ph.D., and when he went to work for Bell Labs, he was the first to implement an artificial reverberation algorithm on a computer. He developed essential shortcuts for producing concert hall reverberation digitally, which employed the use of IIR comb filters, because of their property of exponential decay, and allpass filters to create a sufficient density of reflections needed for realistic reverberation (around 1000 per second).

For lush reverberation, it is necessary to connect a number of unit filters in order to create a sufficient echo density. Schroeder's first reverberation patch included the use of four IIR Comb Filters, and 2 Allpass filters. The comb filters are connected in parallel to minimize spectral anomalies (frequencies passing through one filter, while being attenuated by another), and allpass filters are connected in series because the phase distortion they produce would result in a non-uniform amplitude response were they to be connected in parallel. The purpose of the comb filters is to control the length of the reverb, and the purpose of the allpass filters is to control its intensity. Consequently, the delay (loop) times of the comb filters will be much longer than the delay times of the allpass filters.

It is important to choose delay times that are relatively prime to one another (no common divisor) because echoes will coincide with increased amplitude at multiples of common divisors.

Problems:

There are some inherent problems in this method of digital reverberation. There are peaks in the spectrum, so there is not always of flat response in the reverberation. This can be minimized by using delay times which are prime to one another. Also, the reverberation, while it looks random, is still somewhat periodic, which the ear can track. This wouldn't occur naturally in reverberant spaces, so it sounds wrong to us.

The sound of the reverb can be improved by adding a Lowpass filter to the feedback loop of the IIR Comb Filter. This will attenuate high frequencies more quickly than lower ones, which closely emulates the reverberation properties of concert halls.

## Early Reflections

In a real performance hall, the size and structure of the room affect when and how early reflections reach our ears. Reflections bounce off of the walls, floor, and ceiling of the room, and reach our ear at different times depending on the size of the room, and the location of the sound source.

Generally, the first thing to reach our ear is the direct sound, followed by first-order reflections, which are reflections of that direct sound that have bounced off of the walls, ceiling, and floor of the room. Second and third order reflections have bounced off of two and three surfaces respectively before reaching our ears, and eventually the reflection density reaches a sufficient level for us to just hear a reverberant decay of the sound. The reverberation time is defined as the time it takes the signal to reach a drop of 60 dB in the room.

In a real space, we hear the direct sound first, before we hear any reflections or reverb. As the reverberation builds, it adds to the total level of the sound.

Schroeder's reverberation algorithms generate sufficient echo density to create a good generic reverb, but to simulate detailed acoustic properties of actual performance space, early reflections must be added into the equation. This adds a delay buffer to the signal that models reflections that would normally be produced by sound bouncing off of side walls. Generic reverb sounds pretty much the same anywhere, but early reflections make the sound distinctive.

## Novel Uses of Reverb

Reverb is frequently used for reasons other than modeling realistic spaces. It can be used artistically to suggest distance, to create bizarre spaces, and for a variety of musical uses, such as smoothing transients, gated reverb on snare drums, or sizzling reverb. Reverb also usually contains some control of the amount of wet signal to be mixed with the dry signal.

## Modeling Sound Spaces

Spacial Reverb:

Developed by Kendall and Martens in 1984, spatial reverb creates a 3 dimensional reverb by reproducing first order and second order reflections, along with multiple reverberation streams coming from many different directions. This method effectively places a listener in a specific place in a room with reverb.

## Air Absorption

Reverberation time varies inversely with frequency. Lower frequencies tend to reverberate longer than higher frequencies in real spaces. This is because air absorption attenuates higher frequencies more than low frequencies. Humidity and temperature also affect this absorption. Lower humidity levels absorb less sound, and higher humidity levels tend to absorb more sound.

## Precedence Effect

The auditory system tends to interpret early reflections as a means of distance perception, so we don't usually hear early reflections, except in very large spaces. This explains why small rooms can have a sense of space, but no real reverb. The early reflections are almost as intense as the direct sound, and they reach our ear almost at the same time. The auditory system suppresses the conscious hearing of these reflections until they become sufficiently decorrelated from the direct sound. This seams to me very much like how a comb filter works. At very low delay settings, we hear a comb filter spectrally, but as the delay is increased, we start to hear the reflections caused by the unit delay.

## Distance Perception with Reverberation

The level of reverberation in a space is dependent on the level of the direct sound source, but not on position within the room. Since it's difficult to make sense of early reflections in a concert hall, perception of distance depends more on the ratio between direct sound level and reverb level.

Other ways to create distance effects include lowpass filtering the signal, and lowering its amplitude.

## Local and Global Reverberation

Differentiating between local and global reverberation can add to distance effects in settings with many speakers. Global reverberation is distributed among all loudspeakers equally, where local reverberation is fed only into adjacent pairs of loudspeakers. When a source is close to a listener, the reverberation is distributed equally well in all channels, but as the source moves away, the reverberant signal concentrates in the direction of the source:

local reverberation = 1 - (1/distance)

## Doppler Shift

The Doppler shift effect is an effective radial velocity cue of a source relative to a listener. If the position of the listener remains fixed, the Doppler shift is expressed as:

new pitch = original pitch * [vsound/[vsound - vsource)]

vsound is the velocity of sound (1100 feet/second), and vsource is the velocity of the source relative to the listener.

The Doppler shift effects all frequencies by the same logarithmic interval. This preserves intervalic relationships within the sound.

## Simulating Altitude (Zenith) Cues

Zenith cues can be simulated electronically, giving the impression that a sound is emanating from high places. This is done by filtering the input signal to model the spectrum created by reflections off the head and shoulders. The filter charts used for this type of effect are referred to as Head Related Transfer Functions (HRTF). This type of effect works better with both front and rear loudspeakers.

## Interaural Cross Correlation (IACC)

IACC is the correlation on a scale from 0 to 1 between the sound received in both ears. A IACC of 1 indicates a very focused sound where the sounds received in the left ear are strongly correlated with the sounds in the right ear. An IACC of 0, or close to 0, is representative of a spacious hall because the reverberation heard in the left ear has almost no correlation with the reverberation heard in the right ear. This makes it possible for us to feel "surrounded" by sound, and is generally a characteristic of good concert halls.

Here's a pretty good description of why IACC is important: [url]http://www.ambiophonics.org/Ch_2_ambiophonics_2nd_edition.htm[/url]

To quote Professor Yoichi Ando, (Concert Hall Acoustics, Springer Verlag, 1945), "The IACC depends mainly on the directions from which the early reflections arrive at the listener and on their amplitude. IACC measurements show a minimum at a sound source angle of 55 degrees to the median plane." To translate this, the average person's ears and head are so constructed that a sound coming from 55 degrees to the right of the nose, impinging on the right ear, will not produce a very good replica of itself at the left ear due to time delay, frequency distortion and sound attenuation caused by the ear pinna shape and head obstruction. The IACC value for this condition is typically .36, which is a remarkably good separation for such a situation.

Ando points out that 90 degrees is not better because the almost identical paths around the head (front and back) double the leakage and, therefore, do not decrease the IACC effectively, particularly for frequencies higher than 500Hz.

By contrast, if an early reflection or any sound arrives from straight ahead, the IACC equals one since both ears hear almost exactly the same sound at the same time, and this is desirable for the direct sound from sources directly in front of the listener. That is, the direct frontal sounds should be more correlated than any reflective signals that follow in the first 100 milliseconds or so. As reflections bounce around the hall, the IACC of the reverberant field increases. The rate at which this inter-ear similarity increases determines how good a concert hall sounds when a piece of music with a particular autocorrelation value is being performed. That is why a pipe organ sounds better in a church than in a disco.

## Lexicon Reverb (David Griesinger)

The secret behind the Lexicon reverb is that the reverb delays are modulated to produce a very slight amount of frequency modulation that models the phase jitter that occurs in real rooms. The crossfeeding shown below decorelates the signal.

## Feedback Delay Network

A feedback delay network is a popular new way of creating reverb. It's inception is mostly credited to Jean-Marc Jot in 1982. It gives a maximum "bang for the buck" by creating a feedback matrix that adjusts feedback from any output to any input. Given the small amount of computation time required, it creates a very smooth reverb.

## Reverberation via Convolution

An accurate but computationally intensive means of simulating the reverberation of a given space is to convolve the impulse response of the space with the signal to be reverberated. Direct convolution is not practical because of the amount of computation needed, but fast convolution is possible to calculate in realtime for reverberation effects.

## Granular Reverberation

Reverberation can be attained by convolving an arbitrary input sound with a cloud of sonic grains. This is an adaptation of the atmospheric reverberation effect clouds have in the atmosphere with especially loud noises. "Time Splattering" begins with a dense cloud of sonic grains which are generated by asynchronous granular synthesis (AGS). The reflection contributed by each grain splatters the input sound in time. The color of the reverb is determined by the spectrum of the grains, which is determined by the duration, envelope, and waveform of each grain.

## Waveguide Reverberation

The waveguide approach to reverberation is built on a set of bidirectional delay lines. By connecting a number of waveguides together, one can build a model of the reflection pattern of a concert hall.

## Multiple-stream Reverberation

Multiple-stream reverb spits a signal into several streams, each of which models the local reverberation in a small region of a virtual room. Each stream is implemented with a tapped recirculating delay (TRD) network (comb and allpass filters) tuned for that region of the room. The "spatial reverberator system" is an example of multiple-stream reverberation.