Optimal Rate Filters for Biomedical Point Processes

Rate filters are used to estimate the mean event rate of many biomedical signals that can be modeled as point processes. Historically these filters have been designed using principles from two distinct fields. Signal processing principles are used to optimize the filter's frequency response. Kernel estimation principles are typically used to optimize the asymptotic statistical properties. This paper describes a design methodology that combines these principles from both fields to optimize the frequency response subject to constraints on the filter's order, symmetry, time-domain ripple, DC gain, and minimum impulse response. Initial results suggest that time-domain ripple and a negative impulse response are necessary to design a filter with a reasonable frequency response. This suggests that some of the common assumptions about the properties of rate filters should be reconsidered