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Fig. 3. Graphic representation of microphone order. Polar patterns are shown in two and three dimensions with accom- panying limacon equations and directivity indices (reprinted with permission from Daniel Warren).
the order of the microphone is the power of the cosine term in the limacon equation for directionality, as shown in Fig. 3. While a higher order directional microphone may be capable of more directivity (narrower beam), the problems associated with microphone matching, low-frequency roll- off, internal noise are all magnified with increasing micro- phone (or port) numbers.
The directional systems on the market can be one of the following or some combination thereof: fixed, automatic, and adaptive. In a fixed system, the directional pattern (polar response) has a fixed internal delay and does not change. In the automatic system, an algorithm detects and analyzes acoustic characteristics of environments, and then switches automatically to the appropriate microphone mode (direc- tional or omnidirectional) according to predefined decision
rules. Adaptive refers to the ability of the directional system to change the directional pattern in different noise configu- rations based on measurements made (sampled) in the changing environments and adjusted based on rules pro- grammed in its signal processor. Specifically, the system can “steer” the nulls and/or look direction of the directional pat- tern to the appropriate azimuths (e.g., the azimuth of the noise source) and optimize signal-to-noise (SNR) improve- ment. This adaptivity can be realized independently in dif- ferent frequency channels in a multi-channel adaptive direc- tional hearing aid.
In actuality, it is difficult to specify the real-life direc- tional response of hearing aids with simulated real-ear con- ditions and especially difficult to define with measurements performed in one plane. With the digital hearing aid in posi-
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