Low-Sensitivity Second-Order Digital Filters--Analysis and Design in Terms of Frequency Sensitivity--


IEICE TRANSACTIONS (1976-1990)   Vol.E67   No.8   pp.433-439
Publication Date: 1984/08/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Circuit Theory

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A new procedure to derive low-sensitivity second-order digital filters is presented. This procedure is simple compared to other existing methods. First, a denominator polynomial of a filter transfer function is characterized in terms of ω0 and ωb, which are defined as a center angular frequency and a 3 dB bandwidth of a bandpass filter, respectively. On the other hand, the denominator polynomial is also expressed as a general form including multiplier coefficients and some integer parameters corresponding to existent degrees of freedom. Then the sensitivities of cos ω0 and tan with respect to a multiplier coefficient, which are referred to as frequency sensitivities, are calculated. The integer parameters are determined so that the frequency sensitivities are reduced for small ω0 and ωb. This procedure yields several forms of transfer functions including those of well-known low-sensitivity circuits. One of them is new and the corresponding circuit structures are also given. In addition to its low sensitivity, the new filter has a useful feature; ω0 and ωb are determined independently by each of two multiplier coefficients.