Calculation of the direction of phantom sources - sengpielaudio
 
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Calculation of the direction of phantom source image by
Interchannel Level Difference and Interchannel Time Difference
ILD and ITD
 
● The localization curves for loudspeaker stereo
 
The localisation curves are calculated by interpolation polynomial formula after Lagrange:

Rainbow - sengpielaudio

Enter a value in the left or right box.
The calculator works in both directions of the sign.

Direction of phantom image b1:
 %
 ↔  Level difference Δ L:
 dB
     
100 % phantom source direction equals Δ L = 18 dB
Direction of phantom image b2:
 %
 ↔  Time difference Δ t:
 ms
     
100 % phantom source direction equals Δ t = 1.5 ms

The localisation curves are defined by empirical values after Sengpiel:

Direction of phantom image b1 0 % 25 % 50 % 75 % 100 %
Level difference Δ L 0 dB 3 dB 6.5 dB 11 dB 18 dB

Direction of phantom image b2 0 % 25 % 50 % 75 % 100 %
Time difference Δ t 0 ms 0.23 ms 0.48 ms 0.81 ms 1.5 ms

In 1992, these values of 25 test subjects (students) in the Teldec control room (B & W
Matrix™ 801 Series 3) were determined with test signals of speech, and a Beethoven
string quartet, so without the usual higher-frequency unmusical clicks. There was also
found the little known effect of left localisation shift (left-hand twist stereo hearing).

WolframAudio: http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html

Equations for the level difference and time difference localisation curve
Direction of phantom image b1 in dependence of interchannel level difference Δ L
Direction of phantom image b2 in dependence of interchannel time difference Δ t
Phantom source image - Simonsen and Sengpiel for comparison - 1
Phantom source image - Wittek/Theile and Sengpiel for comparison - 2
Visualization of all Microphone Systems with two microphones
 
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