An iterative least-squares design method for filters with constrained magnitude response in sound reproduction

Filter coefficients determined according to a least-squares criterion are frequently used in applications related to sound zones and adjustable directivity. Without further constraints, the obtained filter coefficients can exhibit very large frequency-domain magnitudes whenever the underlying optimization problem is ill-conditioned. To avoid distortion in the loudspeakers during reproduction, the frequency responses of the reproduction filters can be limited in their magnitudes. However, solving the resulting optimization problem is computationally expensive, which constitutes a problem when large filter lengths or a large number of loudspeaker channels are considered. In this contribution, an efficient previously proposed algorithm is modified such that the filter's magnitude response is constrained. The proposed algorithm uses an approximation in the discrete Fourier-transform domain to yield time-domain filter coefficients. The accuracy of the proposed algorithm is measured by comparing to a state-of-the-art approach for convex optimization considering a free-field scenario. Furthermore, the applicability of the results to real-world scenarios is investigated considering measured impulse responses.