Modal cluster decomposition on two-dimensional frequency domain and its real-time filtering

This paper describes a basic theory for modal cluster decomposition on two-dimensional frequency domain and a design method of real-time filter to extract each decomposed modal cluster. At first, the concept of modal cluster decomposition was introduced. Then, an objective function was derived to determine the sensor placement to realize the modal cluster decomposition. The sensor placement is optimized to place each modal cluster on any selected line in two-dimensional frequency domain. By using the two-dimensional Fourier transform of the array sensor outputs, which are measured at selected optimal sensor locations, desired modal cluster decomposition is realized. In order to extract the desired modal cluster on real-time, we also derived a design method of two-dimensional FIR filter. This filter computes the simple summation of current signals for a spatial direction, and hence there is no time delay to extract the signal of a desired modal cluster.