Advancing support for cause-and-effect models by estimating the kurtosis statistic using fractional-octave-band filters

This paper presents a preliminary method for estimating signal processing parameters that optimally satisfies accuracy and resolution requirements for the sound pressure level and kurtosis level. The kurtosis statistic has long been studied and more recently used for applications in acoustics and vibrations such as architectural acoustics, hearing loss, noise exposure, and accelerated material and structural life testing. The temporal and spectral characteristics of many quantities are evident by time-frequency analysis including hearing, finger sensation, sound diffusion, and reverberation. Some research has conditioned on frequency content while other research has not. Simpson's reversal may potentially adversely affect the models if frequency content is not considered. Modeling techniques which relate cause-and-effect are more likely to result in successful models. Models of human hearing are particularly sensitive to the frequency content because the tonotopic organization of the cochlea induces a cause-and-effect relationship from sound incident on the ear to the basilar membrane. The fractional-octave-band filters specified in ANSI S1.11 and IEC 61260-1 are well developed for conditioning on frequency bands. This paper provides details of the process for optimizing the filter parameters. Additional optimization and testing is described for developing a faster and more accurate method with better support for causal inference.