Design of two IIR digital filters using a single complex filter

It is shown that two properties of rational transfer functions with real coefficients are realized by means of a single complex IIR digital filter. Equivalently, the real and imaginary parts of output from a complex filter for a real input sequence correspond to real coefficient transfer Function respectively, In a real signal processing, a delay operator z(-1) corresponds to a real operation. In this case, a complex transfer function is formed by connecting two real transfer functions with an imaginary unit. These real functions are approximated to the desired properties and are expressed by a complex coefficient transfer function.