# How can one change the virtual position of a sound source with a fixed array of speakers?

I have a question about signal processing:

How to make a person, sitting between array of two loudspeakers (one from the left and one from his right), hear the sound that came from both loudspeakers, from the left side of the left loudspeaker?

I think it's something with the phase and sound-waves interface, but I don't know.

• The question is sufficiently under-specified that I suspect you didn't even understand what you were asked to do. If that is the case the only option you have open to you is to go back to the professor, explain how confused you are and ask for a more complete statement of the problem. If it is not the case then you need to heavily rework this post. – dmckee --- ex-moderator kitten Nov 1 '15 at 17:55
• I am not sure there is an easy answer to this. It is certainly not one that relies on physics, alone, if human hearing is involved. Getting MATLAB to produce a signal in the left channel only is a cs problem, and signal processing to produce proper binaural hearing signals is also not exactly physics. – CuriousOne Nov 1 '15 at 17:58
• I'm not using to much in English,so probably there a mistakes, and I'm sure I understood the problem and I thought maybe I could take some help here in the physics of the problem. thank you anyway. I'm looking in articles of IEEE so if someone think he knew what I should look for there (issues) then it will be helpful. – Yarden Sharabi Nov 1 '15 at 18:12
• I guess you mean "there are 2 signals going to the 2 loudspeakers. How to transform the left signal so that the user has the impression that all is coming from left side". is it this ? – Fabrice NEYRET Nov 1 '15 at 18:20
• in the solution the user will have the impression that all is coming from left side of the left Speaker,I didn't what u mean with "transform the left signal" because there is no priority to the left speaker (at least at the begining ). – Yarden Sharabi Nov 1 '15 at 18:38

This is not trivial, but is routinely done in laboratories and commercial products (like surround stereo systems). If we consider the strictly physical aspects of sound localization in humans (and probably many other living beings who cannot conscientiously orientate their ears), there are two main phenomena to take into account:

1. Interaural time difference (ITD), a slight delay between both ears due to one ear being further away form the source than the other and thus sound has to travel slightly longer to reach it.

This little drawing helps understanding what I mean (source):

So in order to simulate sound coming from one side or the other without moving the speakers, you will need to alter the signal from one or both speakers to try to reproduce this effect. Note that even if you were able to reproduce it correctly, there are many more psychophysics aspects that will get in the way. But as a rough start you could try these equations (c is the speed of sound in air):

$$τ= (a/c)2 sinθ$$

for frequencies below approximately 500 Hz, and

$$τ= (a/c)(θ+ sinθ)$$

above.

That is assuming, among many other things, that people have spherical heads, which is a rather rough estimation.

2. Inter-aural intensity difference (IID), a frequency-specific difference in sound intensity due to the head "shadow" effect, where some frequencies are partially blocked by the head on the path to the ear that is not facing the source.

There is, to date, no analytical way to simulate this effect, you will have to rely on empirically measured transfer functions, such as the Head-Related Transfer Function (HRTF) in the horizontal plane, where the relationship between the angle theta and the frequency response looks like this (source of the picture):

Now you can see that the position of the speakers themselves is not directly linked to the simulation of these effects and it's probably possible to simulate a sound source that appears to be at the left side of the left loudspeaker, that is outside the physical location of the speaker array.