A METHOD OF APPROXIMATING CHARACTERISTICS OF LINEAR-PHASE FILTERS UTILIZING INTERPOLATION TECHNIQUE IN COMBINATION WITH LMS METHOD

The approximation of the gain characteristics of linear phase FIR digi tal filters is reduced to the approximation by cosine polynomials. The refore we can easily obtain an optimum solution under the LMS or Cheby shev error criterion. However the optimum solution does not always mee t practical specifications, especially in the case where the gain is s pecified strictly at some angular frequencies. On the other hand, in s uch a case, it is known that interpolation technique can be suitably a pplied for the approximation mentioned above. However, in this case, w e encounter another difficulty in the approximation caused by interpol ation. In order to overcome the above difficulty, this paper proposes a new method utilizing both of the interpolation and LMS techniques. S ome parameters included in approximating functions are used to satisfy prescribed interpolating conditions and the other parameters are used to minimize the approximation error under the LMS criterion. In addit ion, interpolation technique is extended to include the case in which also higher derivatives are taken into interpolation conditions to mak e smooth interpolation. An example is shown to illustrate the effectiv eness of the proposed method.