Using Bayesian inference for the design of FIR filters with signed power-of-two coefficients

Design of IIR Filters With Bayesian Model Selection and Parameter Estimation

“…Equation (3) represents the square of the errors in both magnitude and phase between the two transfer functions, evaluated at the frequency points of the vector . In [8], a Gaussian likelihood with heuristically determined variance was used instead of the Student's . This could result in more aggressive model comparison results as long as the noise variance can be suitably estimated.…”

“…A common approach is to use a Markov chain Monte Carlo method which generates samples approximating the posterior distribution in frequency [8], [9], [11]. Nested sampling is centered on computing the evidence, which is the quantity that enforces parsimonious model selection.…”

“…This is generally not the case, and often it is advantageous to use the shortest possible filter. A few methods to address this issue have been proposed including a multi-objective optimization formulation [6], selection rules based on information criteria [7], and full Bayesian model selection [8].…”

“…For problems like those in [1]- [4], the desired transfer function and its constraints are expressed in the frequency domain. The authors of [8] advocate the interpretation of engineering design problems as inference, applying the tools of Bayesian inference to design signed power-of-two finite impulse response filters. The problems considered focus on producing filters to meet design criteria instead of the approximation problems found in [1]- [4].…”

Nested sampling-based design of multilayer microperforated panel sound absorbers

“…Adapting the filter design work of Chan and Goggans [5] to the multilayer microperforated panel problem at hand, the error at each frequency ω m is defined as:…”