A new design of low pass filter by Gaussian derivative family

Exploiting the models of human visual system based on Gaussian derivatives and their non-localization property in spectral domain, a new design of low pass filter is proposed in this work. The filter is designed by a weighted combination of the Gaussian derivative family which makes the passband of this filter almost equiripple. This design principle can be extended for the bandpass filter also because of the bandpass nature of the Gaussian derivatives in spectral domain. This work is applied in the design of adaptive digital filters for sigma-delta based ultrasound beamformer