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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, shape (M,)

      Numerator polynomial coefficients. Must be 1-D.

    a array_like, shape (N,)

      Denominator polynomial coefficients. Must be 1-D.

    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.

      Added 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.

  Added in version 0.16.0.

  Array API Standard Support

  `tf2sos` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ⛔
  JAX | ⚠️ no JIT | ⛔
  Dask | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  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. ]])