On 2012-09-24, Fons Adriaensen wrote:
For a line of uncorrelated sources we have to add powers. Imagine the line source as the x-axis, with the origin being the point nearest to you. Let your distance be 'd'. Then the distance to a point 'x' on the line is sqrt(d^2 + x^d). The total power at distance 'd' is the integral from -inf to +inf of 1/(d^2 + x^2), which is 2 * pi / d, i.e. proportional to 1 / d, hence -3dB for each doubling of the distance.
This by the way is precisely the same kind of analysis -- in substance if not in details -- which is used to justify energy decoding over wide ambisonic rigs, by Gerzon, and a square root scaling in summation weights in DSP systems as a function of channels summed together, so as to minimize expected headroom. The statistical assumption it hinges on is that the source signals are independent average gaussian white noise. That assumption frequency-wise breaks down for highways especially at the lower end, a fact which environmental noise models already have to take note of.
-- Sampo Syreeni, aka decoy - [email protected], http://decoy.iki.fi/front +358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 _______________________________________________ Sursound mailing list [email protected] https://mail.music.vt.edu/mailman/listinfo/sursound
