Stable denominators for the simplification of z-Transfer Functions |
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| Authors: | Constantine P Therapos |
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| Institution: | National Technical University of Athens, Department of Electrical Engineering, Athens, Greece |
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| Abstract: | A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m1 and m2 = m−m1 zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m1=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method. |
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