Gaussian or Gaussian derivative filtering is in several ways optimal for applications requiring low-pass filters or running averages. For short filters with lengths of a dozen samples or so, direct convolution with a finite-length approximation to a Gaussian is the best implementation. However, for longer filters such as those used in computing running averages, recursive implementations may be...

We propose a maximum entropy (ME) based approach to smooth noise not only in data but also to noise amplified by second order derivative calculation of the data especially for electroencephalography (EEG) studies. The approach includes two steps, applying method of ME to generate a family of filters and minimizing noise variance after applying these filters on data selects the preferred one wit...

A multi-scale model of edge coding based on normalized Gaussian derivative filters successfully predicts perceived scale (blur) for a wide variety of edge profiles [Georgeson, M. A., May, K. A., Freeman, T. C. A., & Hesse, G. S. (in press). From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision]. Our model spatially differentiates the luminance...

This paper proposes two continuous-time dynamic average consensus filters for networks described by balanced and weakly-connected directed topologies. Our distributed filters, termed 1st-Order-Input (FOI-DCF ) and 2nd-OrderInput Dynamic (SOI-DCF ) Consensus Filters, respectively, allow agents to track the average of their dynamic inputs within an O(ǫ)-neighborhood. The convergence results and s...

The paper discusses the stability and robustness of proportional-integral (PI), proportional-integral-derivative (PID), proportional-integral-derivative-accelerative (PIDA) controller for integral-plus-dead-time (IPDT) plants. To enable implementation measurement noise attenuation, binomial low-pass filters are added to traditional design controllers with ideal transfer functions, impact on rob...

Discrete-time fractional derivative filters (1-D and 2-D) are shown to be well approximated from a small set of integer derivatives. A fractional derivative of arbitrary order (and, in 2-D, of arbitrary orientation) can therefore be efficiently computed from a linear combination of integer derivatives of the underlying signal or image.

Differential motion estimation in image sequences is based on measuring the orientation of local structures in spatio-temporal signal volumes. For this purpose, discrete filters which yield estimates of the local gradient are applied to the image sequence. Whereas previous approaches to filter optimization concentrate on the reduction of the systematical error of filters and motion models, the ...