Bayesian model-based filter design in acoustical signal processing applications
Jonathan M. Botts, Ning Xiang · The Journal of the Acoustical Society of America · 2012
Digital filter design finds applications across many disciplines. Acoustic applications include, but are not limited to, impedance boundary conditions in time-domain wave-based room-acoustics modeling, head-related transfer functions, and loudspeaker equalization. The process of filter design can be approached in a variety of ways. To design a non-standard filter, optimization methods may be used to solve for the coefficients that minimize the difference from a specified transfer function of a prescribed order. Interpreted as a model-based inference problem, a Bayesian framework, realized through the nested sampling algorithm, provides simultaneous optimal coefficient estimates and a filter order selection criterion. The selection criterion implicitly favors simpler models over more complex models, in this case lower-order filters over higher-order filters. Many acoustical applications are well suited to this type design, where low filter order is important, and the desired system response is unattainable with classical, closed-form design techniques. This paper formulates filter design problem as a problem in model-based inference. Then several illustrative examples from acoustical signal processing are used to demonstrate the flexibility of Bayesian digital filter design.