An application of composite complex sinusoidal modeling to the estimation of direction and spectra of an incident plane wave.

Abstract

The present paper proposes composite complex sinusoidal modeling (CCSM) for the estimation of direction and spectrum of an incident sound using a linear array of microphones. Output signals of the microphones in the array are stored in a computer and separated by discrete Fourier transform (DFT) into different frequency components, for all of which spatial sequences are generated. If only one plane wave is present, a spatial complex sinusoidal wave is formed by the sequence, whereas in the case of a plural number of plane waves, the sequence is provided by the sum of the same number of spatial complex sinusoidal waves as that of the plane waves. Direction and spectrum of an incident plane wave are estimated by evaluating amplitude and a rate of phase change (PCR: phase change rate) of the corresponding sinusoidal wave. The directivity pattern obtained by CCSM has no side lobe and gives only a single line which indicates direction and power of the incident plane wave even if the length of the array is of the same order as the wave length of the incident plane wave. In addition, effectiveness of CCSM is confirmed in computer simulation.