scipy.signal.

tf2sos#

scipy.signal.tf2sos(b, a, pairing=None, *, analog=False)[source]#

Return second-order sections from transfer function representation

Parameters:

barray_like: Numerator polynomial coefficients.
aarray_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.
analogbool, optional: If True, system is analog, otherwise discrete.

Added in version 1.8.0.

Returns:

sosndarray: 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. ]])