This example shows several basic aspects of audio signal positioning. The listener occupies a location in the center of a circle, and the position of the sound source is varied so that it remains within the circle. In this example, the sound source is a monaural recording of a helicopter. The sound field is represented by five discrete speaker locations on the circumference of the circle and a low-frequency output that is presumed to be in the center of the circle.

This example requires a 5.1-channel speaker configuration, and relies on the audio channels being mapped to physical locations as follows:

Front left

Front right

Front center

Low frequency

Rear left

Rear right

This is the default Windows® speaker configuration for 5.1 channels. Depending on the type of sound card used, this example may work reasonably well for other speaker configurations.

There are two source blocks of interest in the model. The first is the audio signal itself, and the second is the spatial location of the helicopter. The spatial location of the helicopter is represented by a pair of Cartesian coordinates that are constrained to lie within the unit circle. By default, this location is determined by the block labeled "Set position randomly." This block supplies the input for the MATLAB Function block labeled "Speaker volume computation," which determines a matrix of speaker volumes. The outer product of the sound source is then taken with the speaker position matrix, which is then supplied to the six speakers via the To Audio Device block.

You can also determine the helicopter position manually. To do this, select the switch in the model so that the signal being supplied to the computeVol block is coming from the block labeled "Set position visually." Then, double-click on the new source block. A GUI appears that enables you to move the helicopter to different locations within the circle using the mouse, thereby changing the speaker amplitudes.

The monaural audio source is mixed into six channels, each of which corresponds to a speaker. There is one low-frequency channel in the center of the circle and five speakers that lie on the circumference, as shown in the grey area of the GUI above. The listener is represented by a stick figure in the center of the circle.

The following algorithm is used to determine the speaker amplitudes:

1. At the center of the circle, all of the amplitudes are equal. The value for each speaker, including the low-frequency speaker, is set to 1/sqrt(5).

2. On the perimeter of the circle, the amplitudes of the speakers are determined using Vector Base Amplitude Panning (VBAP). This algorithm operates as follows:

a) Determine the two speakers on either side of the source or, in the degenerate case, the single speaker.

b) Interpret the vectors determined by the speaker positions in (a) as basis vectors. Use these basis vectors to represent the normalized source position vector. The coefficients in this new basis represent the relative speaker amplitudes after normalization.

For this part of the algorithm, the amplitude of the low-frequency channel is set to zero.

3) As the source moves from the center to the periphery, there is a transition from algorithm (1) to algorithm (2). This transition decays as a cubic function of the radial distance. The amplitude vectors are normalized so the power is constant independent of source location.

4) Finally, the amplitudes decay as the distance from the center increases according to an inverse square law, such that the amplitude at the perimeter of the circle is one-quarter of the amplitude in the center.

For more details about Vector Base Amplitude Panning, please consult the references.

Pulki, Ville. "Virtual Sound Source Positioning Using Vector Base Amplitude Panning." *Journal Audio Engineering Society*. Vol 45, No 6. June 1997.