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Generalized Metrics for Constant Directivity

Authors: Sridhar, R., Tylka, J. G., Choueiri, E. Y.
Publication: Forthcoming in the Journal of the Audio Engineering Society (JAES)
Date Accepted: April 15, 2019

Metrics are proposed for quantifying the extent to which a transducer's polar radiation (or sensitivity) pattern is invariant with frequency. As there is currently no established measure of this quality (often called "controlled" or "constant directivity"), five metrics, each based on commonly-used criteria for constant directivity, are proposed:

  1. a Fourier analysis of sensitivity contour lines (i.e., lines of constant sensitivity over frequency and angle),
  2. the average of spectral distortions within a specified listening window,
  3. the solid angle of the frontal region with distortions below a specified threshold,
  4. the standard deviation of the directivity index, and
  5. cross-correlations of polar responses.

These metrics are computed for ten loudspeakers, which are ranked, from most constant-directive to least, according to each metric. The resulting values and rankings are compared and the suitability of each metric for comparing transducers in different applications is assessed. For critical listening applications in reflective or dynamic listening environments, metric 1 appears most suitable, while for such applications in acoustically-treated and static environments, metrics 2 and 3 may be ideal. On the other hand, metrics 4 and 5 appear most suitable for high-amplitude applications (e.g., live sound) in reflective or noisy environments.

Note: This article contains a generalized formulation of the metrics originally presented at the 140th Convention of the Audio Engineering Society in Paris, France on June 4th, 2016. The first and second authors contributed equally to this work.