Authors: Samiya Alkhairy¹,²
¹Massachusetts Institute of Technology (MIT)
²King Abdulaziz City for Science and Technology (KACST)
Background: Auditory filterbanks are fundamental to technologies as well as perceptual models and studies. It is generally desirable to tune these filters to mimic the behavior of the human auditory system. Auditory filters are typically designed by imposing a value for the half-power quality factor or bandwidth of the corresponding pole-pair (or equivalently, the related second order system – SOS). However, we show that this imposed SOS quality factor is not equivalent to the quality factor of higher-order auditory filters. This motivates our goal of developing simple highly accurate methods for the design of auditory filters based on the characteristics of these filters themselves. These characteristics include the peak frequency, peak magnitude, 3 dB bandwidth, 15 dB bandwidth, equivalent rectangular bandwidth, and group delay at the peak.
Methods: To develop our characteristics-based design methods, we derive parameterizations for the auditory filters in terms of sets of the filter characteristics mentioned above. To do so, we derive expressions for the filter characteristics in terms of the filter constant (transfer function pole and exponent), then invert these to derive expressions for the filter constants in terms of characteristics. This allows us to parameterize the filters using these desired characteristics.
Results: The methods are direct, simple, inherently causally-stable, computationally efficient, highly accurate in achieving strict and simultaneous specifications on characteristics, and do not rely on iterative processes with local minima. These properties are collectively not found in existing methods for the design of auditory filter.
Conclusions: In developing the characteristics-based filter design methods, we do not erroneously extrapolate from characteristics-based design of second order filters and instead derives characteristics-based parameterized expressions from first principles as is appropriate for auditory filters of any order. The develop methods enable accurate design of auditory filters based on desired specifications on characteristics. In addition, they enable systematically studying the effect of varying filter characteristics on perceptual tasks and aid in advancing technologies for machine hearing and speech recognition.
