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All-Pole Approximations

  • Hercules G. DimopoulosEmail author
Chapter
  • 3k Downloads
Part of the Analog Circuits and Signal Processing book series (ACSP)

Abstract

In this chapter the all-pole transfer functions are addressed. These are rational functions which in the lowpass case have no zeros at finite positions. The design of normalized lowpass filters from given specifications follows. It is shown that the corresponding gain function (magnitude response) involves a polynomial, the approximating polynomial, which defines the approximation and determines its characteristics. For the classical Butterworth, Chebyshev and Pascal approximations, the corresponding polynomials are employed. Each of these approximations is presented in detail and all design equations are given explicitly. Moreover, their optimal use is explained and demonstrated through several design examples.

Keywords

Transfer Function Chebyshev Polynomial Group Delay Gain Function Chebyshev Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department ElectronicsTechnol. Educ. Inst. of Piraeus (T.E.I.)EgaleoGreece

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