Acoustic Array Systems

5

Nearfield Array Signal Processing Algorithms

This chapter deals with nearfield array signal processing algorithms, including the Fourier NAH, BEM-based NAH (direct and indirect formulations) and ESM (direct and indirect formulations), NESI, and Kalman filter-based algorithms. Comparison of the nearfield algorithms is presented at the end of the chapter.

5.1 Fourier NAH

This section gives a brief account of the traditional Fourier-based NAH. The Fourier NAH seeks to reconstruct a three-dimensional sound field from the two-dimensional hologram data scanned above the source surface (Figure 5.1).

Figure 5.1 Schematic diagram of a microphone array in the near field of the radiated sound from an acoustic source

As the basic form for sources with planar geometries, the Fourier NAH is formulated with Cartesian coordinates. The 2D spatial Fourier transform with respect to x and y is employed to transform a sound field from the spatial domain to the wave number domain, and vice versa:

(5.1)

(5.2)

where x, y, and z are the Cartesian coordinates, d_x and d_y are the lattice spacing of microphones in the x- and y- directions, and k_x and k_y are the wave number components in the x- and y- directions. ...