Stable denominators for the simplification of z-Transfer Functions

✍ Scribed by Constantine P. Therapos

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 552 KB
• Volume: 319
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(85)90003-1

✦ Synopsis

A well-known discrete stability test is used to derivefrom 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 continuedfractionformed with the coejicients 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 m, and m2 = m-m, zeros of D(z), located very near the points z = 1 and z = -1, respectively. In the special case m, = 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.