@MISC{_iv.discrete, author = {}, title = {Iv. DISCRETE VERSION OF THE BODE PROCEDURE}, year = {} }

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Abstract

a) Let us first consider the case where all p o l e s of H(z) are simple. It can be shown that HR(z) in (3) can be expanded in the following form: where k i can be evaluated from The required transfer function H(z) is then identified as an expression which only requires the calculation of { k i} in accor-dance with (9). b) When multiple order poles are involved, the Bode method is computationally somewhat more involved than the Brune-Cewertz method extended by Mitra and Vaidyanathan [2] along with sim-plifications thereof recently proposed by Dutta Roy [6]. However, for the sake of completeness, we note the following steps. The "partial fraction expansion " of HR(z) takes the form k i, + kyrj-,)(z- '- pi) +... + k,(z- '- +c i (z- l- pi)" (11) where the pole at pi is of multiplicity ri and H(z) is deduced therefrom as + 2 c ki, + kicri-,)(Z- p;) + *- * + k,(z-i (I- pi) ri V. EXAMPLE We consider the same example as in [2]. HR(e ' )- 17- 8cos2w '&+,- 1 +cos w + cos2w D ( z) = 17- 4(Z2 + z- ~ ) = 17- 8C2(u/2)