Synthesis of recursive digital filters with prescribed attenuation and group-delay characteristics

A method of synthesizing recursive digital filters with pre- where scribed attenuation and group-delay characteristics is presented. The method depends on the fact that the introduction of complex transmission zeros into the transfer function of the filter network allows independent control of both attenuation and group-delay responses of the filter. An example is presented which clearly demonstrates the improvement in attenuation response obtained when complex transmission zeros are introduced into the transfer function of the filter.