scipy.signal.

ZerosPolesGain#

class scipy.signal.ZerosPolesGain(*system, **kwargs)[source]#

Linear Time Invariant system class in zeros, poles, gain form.

Represents the system as the continuous- or discrete-time transfer function \(H(s)=k \prod_i (s - z[i]) / \prod_j (s - p[j])\), where \(k\) is the gain, \(z\) are the zeros and \(p\) are the poles. ZerosPolesGain systems inherit additional functionality from the lti, respectively the dlti classes, depending on which system representation is used.

Parameters:

*systemarguments

The ZerosPolesGain class can be instantiated with 1 or 3 arguments. The following gives the number of input arguments and their interpretation:

1: lti or dlti system: (StateSpace, TransferFunction or ZerosPolesGain)

3: array_like: (zeros, poles, gain)

dt: float, optional

Sampling time [s] of the discrete-time systems. Defaults to None (continuous-time). Must be specified as a keyword argument, for example, dt=0.1.

Attributes:

dt: Return the sampling time of the system, None for lti systems.
gain: Gain of the ZerosPolesGain system.
poles: Poles of the ZerosPolesGain system.
zeros: Zeros of the ZerosPolesGain system.

Methods

`to_ss`()	Convert system representation to `StateSpace`.
`to_tf`()	Convert system representation to `TransferFunction`.
`to_zpk`()	Return a copy of the current 'ZerosPolesGain' system.

See also

TransferFunction, StateSpace, lti, dlti
zpk2ss, zpk2tf, zpk2sos

Notes

Changing the value of properties that are not part of the ZerosPolesGain system representation (such as the A, B, C, D state-space matrices) is very inefficient and may lead to numerical inaccuracies. It is better to convert to the specific system representation first. For example, call sys = sys.to_ss() before accessing/changing the A, B, C, D system matrices.

Array API Standard Support

ZerosPolesGain 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	⛔	⛔
Dask	⛔	n/a

See Support for the array API standard for more information.

Examples

Construct the transfer function \(H(s) = \frac{5(s - 1)(s - 2)}{(s - 3)(s - 4)}\):

>>> from scipy import signal

>>> signal.ZerosPolesGain([1, 2], [3, 4], 5)
ZerosPolesGainContinuous(
array([1, 2]),
array([3, 4]),
5,
dt: None
)

Construct the transfer function \(H(z) = \frac{5(z - 1)(z - 2)}{(z - 3)(z - 4)}\) with a sampling time of 0.1 seconds:

>>> signal.ZerosPolesGain([1, 2], [3, 4], 5, dt=0.1)
ZerosPolesGainDiscrete(
array([1, 2]),
array([3, 4]),
5,
dt: 0.1
)