Efficient IIR and FIR fan filters

A procedure for designing computationally efficient FIR and IIR fan filters is developed. The fan filters are derived from one-dimensional prototypes which are used in changing sampling rates by a factor of two. The transfer function
B(z)
of the prototype is expressed as
B(z) = T_1(z^2)+zT_2(z^2)
, which leads to a simple expression for the fan filter transfer function. The relation between the passband and stopband deviation requirements of the prototype and the fan filter is derived and employed in the design for meeting two commonly given sets of specifications. A special class of elliptic filters with zeros on the imaginary axis in the
z
plane is shown to yield computationally efficient IIR fan filters. FIR half-band filters are shown to be suitable one-dimensional prototypes for FIR fan filter design. In this case, symmetry constraints on FIR fan filter impulse response are automatically satisfied.