FDTD Simulations of Stereo Speaker Configurations in Small Room

Introduction

In this study the FDTD numerical analysis is used to simulate soundfields in a small room from various loudspeaker configurations.

This is a 2D simulation, and it is understood that floor and ceiling reflections are not modelled. However the human spatial hearing is mainly based on lateral sounds so 2D limitation is not to be considered as too defective.

The analysis signal in this FDTD simulation is a gaussian wavelet. The selected gaussian wavelet has a band pass nature so it can be tuned to a given center frequency. A typical shape of such a waveform is shown in the picture below:

Simulated Stereo Speaker Configurations

The following stereo speaker configurations are included:

• Single Speaker Stereo SSS with matrix x=0.5
• Conventional two speaker stereo triangle
• Three speaker stereo arranged on circle arch with matrix x=0.5
• Three speaker stereo arranged on straight line with matrix x=0.5

In the following simulations the size of the speakers are 20*20 cm, and the room size is 5*3 m. The X and Y scales in the pictures are in meters.

Center Panned Stereo Signal L=1 R=1

Wavefield snapshots at 1000 Hz

Initial wave

Sound field approaches listening area

Sound field approaches more distant listening area

Sound field Animations at 1000 Hz

Time domain animations of the wavefields of the above cases.

Left Panned Stereo Signal L=1 R=0

Wavefield snapshots at 1000 Hz

Initial wave

Sound field approaches listening area

In the case of Single Speaker Stereo SSS the first side wall reflection is to be considered as direct sound.

Sound field approaches more distant listening area

In the case of Single Speaker Stereo SSS the first side wall reflection is to be considered as direct sound.

Sound field Animations at 1000 Hz

Time domain animations of the wavefields of the above cases.

Conclusions

For center panned stereo signal the Single Speaker Stereo SSS produces the cleanest wavefield at the listening position.

For center panned stereo signal the conventional two speaker stereo triangle produces the most distorted wavefield at the listening position.

For center panned stereo signal the three speaker configuration arranged in the curved arch provides improved wavefield at the listening position compared to the two speaker configuration.

For center panned stereo signal the three speaker configuration arranged in the straight line produces better wavefield at the listening position than the curved three speaker configuration.

For side panned stereo signal the first side wall reflection acts as the direct sound for the Single Speaker Stereo SSS. To fulfill this feature a design optimisation of the SSS speaker is to be performed to attenuate the leakage of the direct sound in the side panned signal case.

For side panned stereo signal the wavefield of the Single Speaker Stereo SSS arrives in very large angle relative to median plane. This results in low IACC (Inter Aural Cross Correlation) which can be a benefit.

For side panned stereo signal the two speaker stereo also produces very clean wavefield at the listening position. This is due to only one speaker emitting the sound.

For side panned stereo signal both of the three speaker configurations produces distorted wavefields.

However, the three speaker configuration arranged in the straight line produces most similar performance regardless of stereo panning, even if not the best in all the cases. This could be a benefit in providing a more homogenous performance over the spatial space.

Further reading and References

• Single Speaker Stereo SSS with matrix vector steering SingleSpeakerStereo.html
• Outstanding free mathematical software package for anything imaginable: GNU Octave http://www.gnu.org/software/octave/
• Excellent guide to FDTD method by John Schneider http://www.eecs.wsu.edu/~schneidj/ufdtd/
• AES Preprint: An Optimum Linear-Matrix Stereo Imaging System, Michael Miles http://www.milestech.com/aesimpre.htm