Generalized metrics for constant directivity

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 angular 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 10 loudspeakers that 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 preferable. Furthermore, for high-amplitude applications (e.g., live sound) in reflective or noisy environments, metrics 4 and 5 appear most suitable.