Design of digital fan filters

A design technique is developed for a digital fan-pass filter. The technique involves the rotation of the magnitude response of a recursive half-plane symmetry filter which is, in turn, realized by shifting an ideal two-dimensional low-pass filter. The rotation has the effect of introducing the basic delay unit z
^-1/2
instead of z
^-1
. In order to overcome this effect, two realization schemes are proposed. The concepts underlying these realization schemes may be useful in their own right in realizing any other transfer function containing other basic delay units involving rational power, namely z
^-1/3
, z
^-1/4
, etc. The design of the fan-reject filter is an obvious parallel to that of the fan-pass filter developed in this paper. A design example is worked out, and implementational complexities are discussed.