Theoretically, the complex spectrum circle centroid (CSCC) has the following interesting properties:
(1) Non-linear operation
It should be noted that finding the circle centroid from 
complex
points is not a linear operation on input signals. In this respect,
this method is an entirely different approach from other approaches
based on linear filtering.
(2) Frequency independence
The CSCC principle holds at any of frequency points independently without assuming any frequency characteristics of target and noise signals and microphones. The noise source direction need not to be the same across all frequencies. There is a future possibility of further improvement by assuming the same noise source direction over all frequencies.
(3) Correlated signal and noise
Even if the target signal and noise are statistically correlated, the above discussion still holds: i.e., this method does not need any assumption concerning independence between the target and noise signals. This feature significantly distinguishes the CSCC method from Independent Component Analysis (ICA).
(4) Non-planar wave propagation
Since the present principle is based solely on time differences between target and noise, it is applicable not only to planar, but also to spherical and any other wave propagations if differences in gain is negligible.
(5) Multiple noise sources
In principle, the circle centroid can handle only a single noise source per frequency point. This means that different frequency components are allowed to come from different noise sources as stated in (2). Therefore, even if multiple noise sources exist and if one source is predominant over others per frequency point, the principle still holds and the circle centroid is expected to be noise-reduced spectrum. This situation may really occurr when multiple speech signals overlap where powers, formants, and pitch frequencies may differ from others.
| #noise sources | clean | 1 noise | 2 noises | 3 noises | 5 noises | ||||
| (incident angles [deg]) | (none) | (30) | (30, 270) | (30, 60, 270) | (30,60,120,180,270) | ||||
| #microphones | - | DS | CSCC | DS | CSCC | DS | CSCC | DS | CSCC |
| 1 | 89.4 | 42.2 | -5.7 | -27.4 | -27.5 | ||||
| 3 | 89.4 | 51.1 | 87.1 | 13.2 | 57.0 | -12.2 | 1.0 | -14.8 | -14.0 |
| 4 | 89.4 | 54.1 | 87.9 | 10.5 | 21.6 | -2.6 | 20.1 | -8.1 | 0.3 |
| 8 | 89.4 | 55.1 | 88.0 | 22.9 | 73.6 | 7.7 | 60.6 | 8.2 | 49.0 |
| 16 | 89.4 | 55.7 | 88.0 | 25.3 | 75.1 | 11.2 | 60.6 | 18.6 | 55.5 |