Synthesis of limited-bandwidth minimum-phase filters

A method for designing minimum-phase or minimum-delay filters with an arbitrary complex transfer function inside a finite frequency interval is proposed. The method is based on a result of Krein and Nudel'man (Krein M G and Nudel'man P Ya 1975 Probl. Pereda. Inf. 11 37-60). The filters are divided into two classes, depending on their asymptotic behaviour for high frequencies. For filters with asymptotic value different from zero, a straightforward and completely general synthesis method is proposed, yielding good numerical results. A similar method is shown to be suitable for a limited class of filters whose responses are required to approach zero in a certain sense.