Ξ-filters

A new family of nonlinear digital convolution filters is described having unusual and valuable properties. The response is constant phase over the entire input frequency range and, in some forms, no signal whatsoever is passed beyond the cutoff frequency and side-lobes are identically zero. By simply iterating the transform upon which a Ξ-filter is based without changing the size of the convolution kernel, the cutoff frequency may be varied. Use of Ξ-filters is analyzed and demonstrated as applied to ultrahigh-speed image processing using table-lookup computation.