Calculation of the direction of phantom sources - sengpielaudio
 
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Calculation of the direction of phantom source image by
Interchannel Level Difference Δ L and Interchannel Time Difference Δ t
Phantom source shift between stereo loudspeakers by Δ L and Δ t.
 
ILD = Interaural Level Difference and ITD = Interaural Time Difference has
only to do with signals of natural hearing between a human head.

"Interchannel" = signals between loudspeakers and "interaural" = signals between ears.
 
Localization curves for loudspeaker stereo
 
The localisation curves are calculated by interpolation polynomial formula after Lagrange
 
Equations for level difference Δ L and time difference Δ t localisation curves (German)

Rainbow - sengpielaudio

Enter the 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).
The "stereo base" is the loudspeaker base in stereo reproduction, that is the image width between two speakers in stereo configuration, when the listener is ideally located in a corner of the stereo equilateral triangle.

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

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
Equations for the level difference and time difference localisation curve
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
Duplex-Theorie von Lord Rayleigh (John William Strutt) - German
 
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