
Accession Number : AD0288945
Title : REPRESENTATIONS FOR CLASS K FUNCTIONS
Corporate Author : AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
Personal Author(s) : ZEMANIAN,A.H.
Report Date : 31 AUG 1962
Pagination or Media Count : 1
Abstract : The class k functions represent a generalization of the concept of the positivereal function. This generalization is useful for the purposes of analysis since many properties of networks, whose transfer functions are class k functions, are known. That is, if the transfer function of a network happens to be a class k function, then this transfer function and its corresponding transient responses (such as the unit impulse response and unit step response) will satisfy a number of restrictions. One objective of this investigation has been to construct a definition for the class k functions only in terms of the behavior of these functions in the open righthalf splane, as is done for positivereal functions. This will then allow such functions to have certain types of singularities on the s=jw axis. It is on the basis of this more general definition of class k functions that a successful attack is made on the second and principal objective: to develop a representation for class k functions, which is analogous to Cauer's representation for positivereal functions. (Author)
Descriptors : *CIRCUITS, *COMPLEX NUMBERS, *COMPLEX VARIABLES, *ELECTRICAL NETWORKS, *FUNCTIONS(MATHEMATICS), *INTEGRAL TRANSFORMS
Distribution Statement : APPROVED FOR PUBLIC RELEASE