.Modelica_LinearSystems2.WorkInProgress.Tests.Filters.compareBaseFiltersWithTietzeSchenk

Information

This function compares the filters with the ones from [Tietze2002], pp. 815-852.

In tables Abb. 13.14 on pages 828-834 of (Tietze/Schenk 2002), the filter coefficients are given with respect to normalized filters for a cut-off angular frequency of 1 rad/s. The normalization is performed in such a way that at the cut-off frequency the transfer function has an amplitude of -3db (= 10^(-3/20) = 0.7079457..). In the tables, not the exact -3db value is used but the approximation sqrt(2)/2 (= 0.707106...). Due to "historical" reasons, function baseFilter from the Modelica_LinearSystems library uses -3db for Bessel and Chebyshev filters and sqrt(2)/2 for CriticalDamping and Butterworth filters. Furthermore, the table gives the values only up to 4 significant digits. For these reasons, in this test function the comparison is performed up to 3 significant digits.

Interface

function compareBaseFiltersWithTietzeSchenk
  import Modelica_LinearSystems2.Utilities.Types;
  import ZP = Modelica_LinearSystems2.ZerosAndPoles;
  import Modelica.Utilities.Streams.print;
  import Modelica_LinearSystems2.Math.Complex;
  input String outputFile = "";
end compareBaseFiltersWithTietzeSchenk;