Frequency Transformations in the Analog Domain and Applications

  • Vančo LitovskiEmail author
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 596)


To obtain analog transfer function based on low-pass prototypes one uses frequency transformations. Detailed theory is given for transformation of the zeros and poles of the prototype low-pass transfer function into a new one of a band-pass, high-pass, and band-stop type. Advice is given as to how an all-pass transfer function is obtained from a low-pass prototype. Examples are given with both tables and figures demonstrating the migration of the filter’s characteristic frequencies.


  1. 1.
    Orchard H, Temes GC (1968) Filter design using transformed variables. IEEE Trans Circuit Theory 15(4):385–408CrossRefGoogle Scholar
  2. 2.
    Temes GC, Mitra SK (eds) (1973) Modern filter theory and design. Wiley, New YorkGoogle Scholar
  3. 3.
    Andreani P, Mattisson S, Essink B (2000) A CMOS gm-C polyphase filter with high image band rejection. In: Proceedings of ESSCIRC, pp 244–247Google Scholar
  4. 4.
    Geffe P (1974) Designers guide to active bandpass filters part III. EDN 19(7):46–52Google Scholar
  5. 5.
    Raković BD, Litovski VB (1973) Least-squares monotonic low-pass filters with sharp cutoff. Electron Lett 9(4):75–76CrossRefGoogle Scholar
  6. 6.
    Zolotarev EI (1877) Application of elliptic functions to problems about functions with least and greatest deviation from zero. Zapi Imp Akad Nauk St Petersburg 30(5) (in Russian).
  7. 7.
    Papoulis A (1958) Optimum filters with monotonic response. Proc IRE 46:606–609CrossRefGoogle Scholar
  8. 8.
    Papoulis A (1959) On monotonic response filters. Proc IRE 47:332–333Google Scholar
  9. 9.
    Fukada M (1959) Optimum filters of even orders with monotonic response. IRE Trans Circuit Theory 6(3):277–281CrossRefGoogle Scholar
  10. 10.
    Topisirović D, Litovski V, Andrejevic Stošović M (2015) Unified theory and state-variable implementation of critical-monotonic all-pole filters. Int J Circuit Theory Appl 43(4):502–515CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Elektronski FakultetNišSerbia

Personalised recommendations