scipy.signal.

zpk2tf#

scipy.signal.zpk2tf(z, p, k)[source]#

Return polynomial transfer function representation from zeros and poles

Parameters:

zarray_like: Zeros of the transfer function.
parray_like: Poles of the transfer function.
kfloat: System gain.

Returns:

bndarray: Numerator polynomial coefficients.
andarray: Denominator polynomial coefficients.

Notes

Array API Standard Support

zpk2tf 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

The CuPy and JAX backends both support only 1d input.

See Support for the array API standard for more information.

Examples

Find the polynomial representation of a transfer function H(s) using its ‘zpk’ (Zero-Pole-Gain) representation.

\[H(z) = 5 \frac { (s - 2)(s - 6) } { (s - 1)(s - 8) }\]

>>> from scipy.signal import zpk2tf
>>> z   = [2,   6]
>>> p   = [1,   8]
>>> k   = 5
>>> zpk2tf(z, p, k)
(   array([  5., -40.,  60.]), array([ 1., -9.,  8.]))