ON THE DESIGN OF RECURSIVE DIGITAL-FILTERS CONSISTING OF A PARALLEL CONNECTION OF ALLPASS SECTIONS AND DELAY ELEMENTS

This paper presents a general method for the design of selective syste ms, implemented with two coupled allpasses, one of which consists part ially or completely of delay elements. After reviewing some properties of this kind of filters, an iterative design procedure is presented, which deals with the phase difference of the two allpasses. The phase approximation problem is formulated and it is shown that its Chebyshev solution is unique and can be characterized as usual. The solution ca n be found by a Remez-like algorithm, starting with an appropriate ini tial solution, which can be found by approximating the corresponding g roup delay, as will be shown separately. The method will be illustrate d by some examples.