Mid Sweden University

Cardioid microphones/hydrophones have been commonplace in practical acoustics. Indeed, cardioid sensors are widely obtainable in retail as diverse commercial models produced by numerous manufacturers. A cardioid sensor has a highly directional gain pattern of &#x03B1; + (1 - &#x03B1;)cos(&#x03B3;), where &#x03B1; represents the sensor&#x2019;s cardioidicity index, and &#x03B3; denotes the impinging wavefront&#x2019;s spatial angle incident upon the cardioid sensor&#x2019;s axis. This paper is the first in the open literature to investigate the &#x201C;spatial matched filter" beam-pattern obtainable from two such cardioids that lie in perpendicular colocation. Such a bi-axial cardioid pair is worth investigating because (i) their diverse orientation successfully realizes two-dimensional (azimuth-polar) directivity with only two sensors, (ii) their spatial colocation is advantageous for <italic>physical compactness</italic> and also for the <italic>decoupling</italic> of the data&#x2019;s time-and-frequency dimensions from the azimuth-and-elevation directional dimensions to simplify signal-processing computation. This present investigation, however, uncovers that this beam-pattern generally peaks away from the nominal preset &#x201C;look direction", but algorithmic mitigation is made possible by this paper&#x2019;s pre-steering formula derived here to judiciously pre-adjust the beamformer&#x2019;s nominal &#x201C;look direction". Further action-able insights are provided in this paper for the hardware system engineer to pre-select the sensors&#x2019; cardioidicity index &#x03B1; for maximum steerability and freedom from sidelobes.