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# scipy.signal.tf2sos

scipy.signal.tf2sos(b, a, pairing=None, *, analog=False)

  Return second-order sections from transfer function representation

  Parameters:
    b array_like

      Numerator polynomial coefficients.

    a array_like

      Denominator polynomial coefficients.

    pairing{None, ‘nearest’, ‘keep_odd’, ‘minimal’}, optional

      The method to use to combine pairs of poles and zeros into sections. See `zpk2sos` for information and restrictions on pairing and analog arguments.

    analog bool, optional

      If True, system is analog, otherwise discrete.

      New in version 1.8.0.

  Returns:
    sos ndarray

      Array of second-order filter coefficients, with shape `(n_sections, 6)`. See `sosfilt` for the SOS filter format specification.

  See also

  `zpk2sos`, `sosfilt`

  Notes

  It is generally discouraged to convert from TF to SOS format, since doing so usually will not improve numerical precision errors. Instead, consider designing filters in ZPK format and converting directly to SOS. TF is converted to SOS by first converting to ZPK format, then converting ZPK to SOS.

  New in version 0.16.0.

  Examples

  Find the ‘sos’ (second-order sections) of the transfer function H(s) using its polynomial representation.

  \[H(s) = \frac{s^2 - 3.5s - 2}{s^4 + 3s^3 - 15s^2 - 19s + 30}\]

      >>> from scipy.signal import tf2sos
      >>> tf2sos([1, -3.5, -2], [1, 3, -15, -19, 30], analog=True)
      array([[  0. ,   0. ,   1. ,   1. ,   2. , -15. ],
             [  1. ,  -3.5,  -2. ,   1. ,   1. ,  -2. ]])