Noncausal digital filters with antisymmetrical impulse response

A new design and realization technique for noncausal digital filters with antisymmetrical impulse response is proposed. The resulting filter has purely imaginary frequency response suitable for realizing ideal Hilbert transformer and differentiator. It is shown that the antisymmetrical impulse response noncausal filter can be decomposed into two identical subfilters and two first order nonrecursive sections. The design requirements are translated to magnitude response specifications of the identical subfilters. The filter is then easily obtained using many well known design techniques based on magnitude response. A design example of Hilbert transformer is shown.