Primarily, we assume that acoustic characteristics (gains,
directivities, etc.) of microphones are identical (or can be equalized
by adjusting gains and delays at each frequency). If the target signal
propagates and arrives at microphones simultaneously at time
while the noise signal arrives with different time delays
as shown in Figure
1, the observed signal at the -th
microphone is represented by:
The short-time Fourier transform of the -th microphone input signal
is given by
Geometrically, Eq. (2) implies that lies on a circle of radius with a centroid at on the complex spectrum plane. The complex spectrum of target signal is restored by finding the centroid of the circle on which complex points lie. We call this method of estimating the target signal spectrum ``Complex Spectrum Circle Centroid (CSCC) method.''
In contrast, the Delay-and-Sum (DS) method uses the center of gravity (arithmetic mean) of microphone inputs: .