Journal of Optimization Theory and Applications

, Volume 6, Issue 5, pp 356–363 | Cite as

Simultaneous determination of ordering and amplifications of cascaded subsystems

  • Shlomo Halfin
Contributed Papers


Letn linear, time-invariant subsystems with transfer functionsT1(s),T2(s),...,T n (s) be given. We are required to cascade these subsystems into a system with the transfer functionT(s)=kT1(s)T2(s) ...T n (s), wherek>0, by determining the order of the subsystems and choosing for each subsystemi an amplification factork i such thatk=k1k2 ...k n .We do this using the following optimality criterion: Given a setI, minimize the ratio of the maximum and the minimum of all the absolute values of all the intermediate outputs inI, for a flat input. This criterion is applicable in cases where the intermediate outputs should not be overdriven or underdriven. In particular, the method is applicable to the problem of determining an optimal ordering and intermediate amplifications of cascadedRC-active filters.


Simultaneous Determination Optimality Criterion Intermediate Output Flat Input 
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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  1. 1.
    Lueder, E.,Cascading of RC-Active Two-Ports in Order to Minimize Inband Losses and to Avoid Distortion, Paper presented at the IEEE International Conference on Communications, Boulder, Colorado, 1969.Google Scholar
  2. 2.
    Gray, F., Patent No. 2-632-058, 1953.Google Scholar

Additional Bibliography

  1. 3.
    Bellman, R.,Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.Google Scholar
  2. 4.
    Halfin, S.,An Optimization Method for Cascaded Filters, The Bell System Technical Journal, Vol. 49, No. 2, 1970.Google Scholar

Copyright information

© Plenum Publishing Corporation 1970

Authors and Affiliations

  • Shlomo Halfin
    • 1
  1. 1.Bell Telephone LaboratoriesHolmdel

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