Acoustic Array Systems

6

Practical Implementation

This chapter outlines practical considerations frequently encountered in implementation projects, including inverse filter design, multi-channel fast filtering, post-processing, choice of DOR and lattice spacing, virtual microphone technique, choice of RD, optimization of sensor deployment, and system integration and experimental arrangement.

6.1 Inverse Filter Design

In general, inverse problems are based on an associated forward problem. This forward problem underlying NAH is the sound field model that represents the acoustical field radiated from a sound source. Acoustic excitation is employed as the system input to be reconstructed. This section gives an introduction to important issues associated with inverse problems of NAH.

6.1.1 Model Matching: Ill-Posedness and Regularization

The problem of ESM in Chapter 5 can be regarded as a model-matching problem depicted in Figure 5.23. Similar to the deconvolution process in NAH, the system matrix G is usually ill-conditioned. This calls for the need of optimization with proper regularization. The problem considered here can be put into the following optimization formalism:

(6.1)

where symbolizes the Frobenius norm [1] defined as, for a matrix ,

(6.2)

Hence, the minimization problem of Frobenius-norm can ...