Generalized Approximation

Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 210)


So far in this book, we have restricted our discussion of filter transfer functions to those of the minimum-phase or quasi minimum-phase types. This has been done in order to obtain low-sensitivity structures which have passive counterparts. The price to pay for this highly desirable attribute, however, is that there exists an upper bound on the fraction of the passband over which phase linearity can be maintained, once the amplitude selectivity has been specified. For most applications this upper bound is not too restrictive since we have demonstrated that one can achieve an excellent approximation to phase linearity over 85% of the passband with moderate order filters. Nevertheless, it is always desirable to have at our disposal a most general technique for the simultaneous approximation of amplitude and phase which is not subject to these constraints. To this end, we have to drop the minimum-phase nature of the transfer functions, and sacrifice the low-sensitivity property of the structures for increased flexibiliy. In this chapter, an approximation technique of considerable generality is given for the derivation of non-minimum-phase transfer functions which satisfy simultaneous conditions on the amplitude and delay responses. These are realizable in cascade form.The technique represents the most comprehensive one available for the solution of the simultaneous amplitude and phase approximation problem and leads to a large family of stable transfer functions [12].


Transfer Function Transmission Zero Stopband Attenuation Stringent Specification Passband Width 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  1. 1.Worcester Polytechnic InstituteUSA

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