Acoustical Models

The acoustic model is parametric and divides the signal path from a virtual sound source to the listener into:

1. Direct sound
2. Early reflections
3. Reverberation tail

The direct sound is the sound wave that propagates directly from the sound source to the listener.
If the sound source and the listener are in an anechoic environment (Free Field condition) then the only signal path is the direct sound.
In other environments the surroundings affect the sound wave reaching the listener. This influence can be modelled as discrete reflections for wave lengths smaller than the dimensions of the surroundings.

In a room the reflections from the walls are reflected themselves and in this way an infinite response is created. Each time a wave is reflected some energy is absorbed by the wall and so the energy of the wave is getting lower and lower. The amount of energy absorbed depends on the wall material, the angle of incidence and its frequency dependent. Only the first reflections, called early reflections, are modelled while the remaining part of the response is modelled as diffuse field reverberation.

The figure below sketches the direct wave path, the path of a wave reflected once (first order reflection) and the path of a second order reflection.

This can be visualised by looking at the impulse response from an actual room:

IMPULSE RESPONSE FROM A ROOM

The first high peak in the figure above represents the response of the direct wave while the remaining part is reflections.
The figure below plots of the first 75 ms of the response. Here it is easier to see direct the wave and the early reflections. It is also evident that the amount of reflections increases rapidly until they no longer can be considered discrete reflections. Once this happen the reflections are regarded to come from all directions, which is the part that is called the reverberation tail. The sound field is then diffuse.

FIRST PART OF ROOM IMPULSE RESPONSE

Basic Sound Wave Model
This section deals with the modelling of sound waves in the free field situation.
The sound sources are modelled as point sources. This model holds in many situations in real life. When the physical extend of the sound source is small compared to the distance to the listener it is a usable model.

A point source sends out spherical sound waves. But in relation to HRTF's the wave can be regarded as plane for distances above 2 meter. Above this distance the difference in Interaural Time Delay (ITD) between spherical and plane sound waves is negligible because it is no longer detectable by the human hearing (ITD error being less than approximately 20 micro seconds). For plane waves the HRTF's are independent of distance.

The human distance perception is based on both absolute cues and relative cues. To detect the absolute cues it is required that the listener has some kind of a priori knowledge about the sound source. Relative cues are present when the distance between the listener and the sound source changes.

Modified sound source model
The sound source model can be modified to fit natural sound sources. This is done by applying a radiation pattern for the source. The behaviour is still that of a point source but the radiated energy depends on the direction to and the orientation of the source. The radiated energy may again depend on frequency.

In the current 3D Sound engine all sound sources are regarded omni directional.

Reflection model
The reflections are modelled as discrete sound waves. In this way the free field model can also be used on the reflections but they will of course still depend on the geometrical shape of the enclosure/room.

When a sound wave is reflected against a wall the wall absorbs some energy. The reflections are modelled as locally reacting and frequency dependent. Only specular reflections are considered.

Each wall material has its own frequency dependent absorption coefficient and a database of filters is obtained from the measured absorption coefficient in 8 octave bands from 62,5 Hz to 8 kHz. Wide range materials are supported.

Calculation of early reflection wave properties
The properties of the reflections are found by using a room simulation algorithm where a mirror source technique is used. Each mirror source corresponds to a reflected sound wave. The algorithm finds the walls by which the mirror sources are reflected, the angles of incidence and the radiation angle. The mirror sources are checked for visibility.

The properties of the reflections are fed to a number of instances of the basic BSE, which will handle the sound rendering.

Reverberation
Two methods are used to create the reverberation tail.

One method is using a BRIR measurement made in a room that have similar acoustics as the one being modelled. The diffuse field part of the BRIR is extracted and by use of a fast convolution technique the dry sound signal is filtered with the diffuse field BRIR. The BRIR filtered signal is added to the output signal from the basic BSE instances.

The second method is similar to the first except a professional reverberation unit is used to simulate the reverberation tail. Using this approach the selected reverberation will have to rely on expert listening. The result may however be just as convincing as using a BRIR measurement.