FDTD Simulations of Single Speaker Stereo SSS

Introduction

I wrote my own code from scratch for 2D FDTD simulations. It was a nice weekend project. I must admit, though, that it took more than a one weekend :)

The simulation code is running on Octave platform.

With FDTD (Finite Difference Time Domain) method it is possible to simulate propagating wave fields in a medium.

Here the focus is in simulating sound fields from the Single Speaker Stereo SSS in a small room to gain more understanding on its performance in a typical listening room.

Emphasis is on first room reflections and how reflected waves would be presented to the listener in a room.

This is a 2D simulation, and it is understood that floor and ceiling reflections are not modelled, but it is believed to provide useful insight and intuition for further development and optimisation of Single Speaker Stereo SSS.

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:

In the following simulations the size of the SSS speaker is 20*20 cm, and the room size is 5*3 m. The SSS speaker is placed in the longitudal symmetry line of the room. The speaker distance to the front wall is 1 m. The X and Y scales in the pictures are in meters.

Center Panned Stereo Signal L=1 R=1 for SSSx5

Wavefield snapshots at 200, 500, 1000 and 2000 Hz

Initial wave

For matrix x = 0.5 the speaker element signals are for center panning: Left element 0.5, center element 1 and right element 0.5.

Radiation pattern before reflections

Notice the maximum radiation is towards the listening area.

Direct sound approaches listening area

Notice the direct sound is clean from wall reflections.

First side wall reflection approaches listening area

Notice the two side wall reflections arrive at the listening area at very high incidence angle.

Animations at 200, 500, 1000 and 2000 Hz

Time domain animation of the wavefields of the above cases.

Left Panned Stereo Signal L=1 R=0 for SSSx5

Wavefield snapshots at 200, 500, 1000 and 2000 Hz

Initial wave

For matrix x = 0.5 the speaker element signals are for left panning: Left element 1, center element 0.5 and right element -0.5.

Radiation pattern before reflections

Notice the maximum radiation is towards bottom left and minimum radiation is towards bottom right.

Direct sound approaches listening area

Notice in this case the direct sound should be weak and is a subject of design optimisation.

First side wall reflection approaches listening area

Notice the reflection from the left is very strong and the reflection from the right is very weak.

Also notice the reflection arrives at the listening area at very high incidence angle, which results in low IACC (Inter Aural Cross Correlation) which in turn results in a spacious and enveloping sound.

Animations at 200, 500, 1000 and 2000 Hz

Time domain animation of the wavefields of the above cases.

Conclusions

FDTD simulations are a great visualisation tool to learn the behaviour of the wave fields. The effects of reflections and diffractions can be studied using this method.

The Single Speaker Stereo SSSx5 with matrix x = 0.5 provides a stereophonic sound field in a small room. This is achieved by using the signal steering linear matrix at the loudspeaker and by employing the listening room side walls as projection screens.

For center panned signal the SSSx5 delivers a dominant wave field from the central location which is clean from side wall reflections.

For side panned signal the SSSx5 delivers a strong side wall reflection from the panned side. The reflection arrives from a high incidence angle which results in a low IACC.

In the case of the side panned signal the direct sound from the speaker to the listening area should be minimised. There are some design factors involved to achieve this in an optimum manner.

Further reading and References

• 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/