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Two methods for the construction of transfer functions of digital integrators

Two methods for the construction of transfer functions of digital integrators

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The letter describes two methods for the construction of digital-integrator transfer functions with an ideal phase characteristic. The first is based on the approximation of the function ln z by means of continued fractions, and the second consists in the approximation based on the principle of the impulse-response invariance. The transfer functions can be approximated to in both cases by nonrecursive transfer functions in the bilateral z transformation.

References

    1. 1)
      • J.T. Tou . (1959) , Digital and sampled-data control systems.
    2. 2)
      • A.N. Khovanski . (1956) , Application of continued fractions and their generalisation in numerical analysis.
    3. 3)
      • R. Vích . Approximation in digital-filter synthesis based on time reponse invariance. Electron. Lett. , 442 - 444
    4. 4)
      • D.F. Lawden . The functions Σn=1∞nzzn and associated polynomials. Proc. Cambridge Phil. Soc. , 309 - 314
    5. 5)
      • Vích, R.: `Tables of zeros of z-transforms Σ', Report 40, 1968.
    6. 6)
      • Grebe, H.: `Synthese digitaler Systeme für die Zwecke der digitalen Simulation', 1969, Dissertation, Technische Universität Berlin.
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