ABSTRACT
What type of frequency response function can be postulated that will meet the required specifications and — at the same time — be realizable: constructible with a specified catalog of elements? The answer depends upon the types of elements allowed. For instance, if one allows pure delays with a common delay time, summers, and scalar multipliers, a trigonometric polynomial will work; this, however, will cause the gain function to be repeated in a periodic manner. If this is permissible, one can then realize the filter in the form of an FIR digital filter or as a commensurate transmission line filter — and, in fact, it can be realized in such a fashion that the resulting phase behavior is precisely linear. If one fits the required behavior with a rational trigonometric function, a function that is the ratio of two trigonometric polynomials, an economy of hardware will result. The phase, however, will unfortunately no longer be linear. These issues are discussed at greater length in [1].
