Meeting Topic: On the Use of Signal Modeling for the Purpose of Study and Design of Multi-Microphone Systems
Speaker Name: Plamen Ivanov, Motorola Mobility
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Meeting Location: Shure Incorporated, 5800 W. Touhy Ave, Niles, IL 60714
The talk began with a review of the main techniques for multi-microphone arrays.
A "delay and sum beam-former" typically uses a large number of microphone elements to achieve a tight, steerable pickup pattern. The signal from each element is individually delayed using DSP such that for the desired pickup direction, all microphone elements add together coherently. For all other directions, these elements add together incoherently.
Delay can be applied at a finer resolution than the sample period of the digital audio by applying a fractional delay filter. Two common methods of implementing a fractional delay filter are FIR and Lagrange interpolation. Inevitably, the pickup pattern of such an array is frequency dependent.
A differential microphone array is typically composed of only a few microphone elements. Two microphone elements separated by some distance can be used to form a directional pickup pattern by delaying one of them and subtracting the two signals. With two microphone elements, all 1st-order polar patterns can be generated: cardioid, figure-of-8, hyper-cardioid, etc.
Mr. Ivanov then went on to describe more complex patterns that can be formed from multiple microphone elements using the differential approach. Dipole elements, for example, can be combined to form a quadrupole or a 2nd-order dipole.
The remainder of the discussion focused on modeling approaches for designing and validating microphone arrays. The approaches discussed were: physical model, mathematical model, and a boundary element model.
The physical model is perhaps the most straightforward way of analyzing a design, but tends to be expensive, time consuming, and is difficult to make any changes to. Mathematical and computer modeling have the advantage of allowing many configurations to be tested with little additional time or expense.
The simplest mathematical model is that of the transparent array in a free field. That is, the simulated microphone elements are infinitesimally small points in free space without any acoustic reflection or refraction. Despite its simplicity, this is often helpful as a first-round design tool.
More sophisticated computer modeling tools are finite element modeling (FEM) and boundary element modeling (BEM). Applied properly, BEM can produce very accurate results that are consistent with physical measurements. One advantage is that the BEM can properly account for what Plamen calls the "other" HRTF. That is, the "handset related transfer function" (when talking about mobile phones).
Written By: Ross Penniman