A Method of Approximating Characteristics of Linear Phase Filters Utilizing Interpolation Technique in Combination with LMS Method

Yoshiro SUHARA  Takashi MADACHI  Tosiro KOGA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.6   pp.911-916
Publication Date: 1993/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Papers Selected from 1992 Joint Technical Conference on Circuits/Systems,Computers and Communications (JTC-CSCC'92))
Category: Methods and Circuits for Signal Processing
digital filter,  linear phase,  digital signal processing,  

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The approximation of the gain characteristics of linear phase FIR digital filters is reduced to the approximation by cosine polynomials. Therefore we can easily obtain an optimum solution under the LMS of Chebyshev error criterion. However the optimum solution does not always meet practical specifications, especially in the case where the gain is specified strictly at some angular frequencies. On the other hand in such a case, it is known that interpolation technique can be suitably applied for the approximation mentioned above. However, in this case, we encounter another difficulty in the approximation caused by interpolation. In order to overcome the above difficulty, this paper proposes a new method utilizing both of the interpolation and LMS techniques. Some 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 addition, interpolation technique is extended to include the case in which also higher derivatives are taken into interpolation conditions to make smooth interpolation. An example is shown to illustrate the effectiveness of the proposed method.