Why is directional noise correlated noise?

[CantorSet]

Hi everyone,

This is not a homework question but I question I have from reading a signals processing paper on acoustics.

Suppose there is a sound source in a room $$S(t)$$ and two microphones $$X_1(t)$$ and $$X_2(t)$$. Then the standard acoustic propagation model has that

$$X_1(t) = a_1S(t-\tau_1)+n_1(t)$$

and

$$X_2(t) = a_2S(t-\tau_1)+n_2(t)$$

where $$a_i, \tau_i, n_i$$ account for signal attenuation due to distance, time delay due to distance and noise, respectively.

But the paper says that if we have directional noise in the room (like a ceiling fan), then the noise at the two microphones is correlated, that is [tex]Corr(n_1(t),n_2(t)) \neq 0 [/itex]. <br /> <br /> But it seems to me the directionality isn't what's causing the correlation, but more the fact that the noise comes from a fan. That is, if we had an "omnidirectional" fan in the center of the room, the noise between the two microphones would still be correlated.<br /> <br /> Also, how does one mathematically represent noise that is directional?[/tex]

 

[fleem]

In this context, I'd have to assume that by "directional", they simply mean the sound has one point source, as you say (and not that it is anisotropic!). On a side note, practically speaking there will be notable multipath, making things more difficult.

By the way, that Tau in the second equation should be tau sub 2, not Tau sub 1 (unless the microphones are the same distance from the sound source)

To mathematically describe noise that comes from a point source (described here as "directional"), treat it as if it were just another signal source term, albeit an undesirable one.

 

[CantorSet]

In this context, I'd have to assume that by "directional", they simply mean the sound has one point source, as you say (and not that it is anisotropic!). On a side note, practically speaking there will be notable multipath, making things more difficult.

By the way, that Tau in the second equation should be tau sub 2, not Tau sub 1 (unless the microphones are the same distance from the sound source)

To mathematically describe noise that comes from a point source (described here as "directional"), treat it as if it were just another signal source term, albeit an undesirable one.

Thanks for your help, Fleem.