Design of IIR Filters With Bayesian Model Selection and Parameter Estimation

Abstract

Bayesian model selection and parameter estimation are used to address the problem of choosing the most concise filter order for a given application while simultaneously determining the associated filter coefficients. This approach is validated against simulated data and used to generate pole-zero representations of head-related transfer functions.

Nested sampling in practice

“…Particularly with regard to the latter, Skilling [6] reports a theoretical uncertainty estimate based on the population size and accumulated evidence (information gain). However, according to a few recent references [7,10], when the sampling is repeated many times on the same data, the spread of evidence values can be substantially greater than the estimated uncertainty and even greater than the penalty for increasing model complexity. Consistency of estimated evidence should depend on the complexity of the sampling problem, the amount of exploration, and the type of exploration.…”

“…The two test problems are taken from [7] and [8]. The first is described as IIR filter design, but can be more generally interpreted as fitting a pole-zero system to complex transfer function data.…”

“…These intensities should approximate the beampattern model in Equation 7. In this small study, the data are all synthetic with additive Gaussian noise.…”

“…Perhaps the largest issue evident in recent publications [7,10], is the potential variability of evidence estimates. Often, the estimated uncertainty from a single run [6] is far smaller than variability between repeated runs.…”

Hybrid convex combinations for IIR system identification.

“…Of course, this case alone suces to establish that the AF tting does not improve by simply that they can rarely be modelled exactly by nite order rational functions [12]. Note that order estimation is a fruitful eld of study by itself (e.g., [133] or [132]). Conversely, albeit it could not be a major limiting factor for FIR AFs and variance relation arguments developed by Sayed [5], but his studies refers to another context and do not comprise the peculiarities of rational systems.…”