MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

92 Applications
(a)
(b)
Figure 3.20: (a) Projective Plane of Order 2. (b) Binary Matrix Representation.
(c) Hamming Code of Length 7. [286]
represent lines, the columns represent points and the presence of a 1 indicates
that a point lies on a line or, equivalently, a line contains a point (0 otherwise).
The Hamming code of length 7, which contains 8 codewords, is obtained by
taking the complement of the rows of this matrix and appending the zero
codeword (Figure 3.20(c)). It has minimum Hamming distance d = 4 and is a
single-error-correcting code [286].
Application 21 (Equilateral Triangle Rule (Speaker Placement)).
Stereo playback assumes a symmetrical loudspeaker and listener arrangement
with a 60 ◦ angle between the loudspeakers and corresponding to an equilateral
triangular configuration (Figure 3.21) [208].
Application 22 (Equilateral Triangular Microphone Placement). Hioka
and Hamada [173] have explored an algorithm for speaker direction tracking using
microphones located at the vertices of an equilateral triangle (Figure 3.22).
In teleconferencing and remote lecturing systems, speaker direction tracking
is essential for focusing the desired speech signal as well as steering the
camera to point at the speaker. For these applications, the accuracy should be
spatially uniform for omni-directional tracking and, for practical purposes, a
small number of microphones is desirable. Both of these objectives are achieved
by the integrated use of three cross-spectra from the equilateral triangular microphone
array. Computer simulations and experimental measurements have
confirmed that this array possesses uniform omni-directional accuracy and does
not lose track of the speaker even if he/she moves abruptly.
(c)