On the upper bounds of the equivalent oscillator and notch-filter circuits: a non-commutative group theoretic approach
P. Raadhakrishnan, A.E. Yagle, Bapuji Rao, J.E. Dorband · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 1992
It is shown that the problem of synthesizing equivalent oscillators and notch filters from the knowledge of a given parent circuit is identical to that of finding the isomorphisms of a noncommutative group. It is also shown that many of the results established by earlier methods can easily be explained using the theory developed. The results derived show that earlier results do not lead to the best possible upper bound. The corrected upper bound is derived by counting the numbers of the noncommutative group. A well-known family of circuits is used to illustrate the theory developed.>