Finite-Array Correction

In practice, it is necessary to truncate an array to finite bounds. This causes reconstruction error analogous to the error obtained when restoring a continuous-time signal from a finite segment of its samples. Thus, most of the error occurs for sources near the edges of the array (i.e., arriving from the maximum angles-of-arrival supported). This error can be reduced by compensating for the missing contributions from the truncated ``sampling kernels''. From this point of view, the error is equivalent mathematically to the ``Gibbs phenomenon,'' and many forms of ``windowing'' and ``apodization'' have been advanced to address the issue (Smith, 2011).¹⁵One can also formulate a customized optimization that maximizes perceptual criteria; for this problem, linear programming formulations may suffice for correcting amplitude error.¹⁶A Hann window is used for array windowing in the Sound Field Synthesis Toolbox (Wierstorf and Spors, 2012).¹⁷