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.


*system : arguments

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

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.


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.


>>> from scipy import signal

Transfer function: H(s) = 5(s - 1)(s - 2) / (s - 3)(s - 4)

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

Transfer function: H(z) = 5(z - 1)(z - 2) / (z - 3)(z - 4)

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


A State matrix of the StateSpace system.
B Input matrix of the StateSpace system.
C Output matrix of the StateSpace system.
D Feedthrough matrix of the StateSpace system.
den Denominator of the TransferFunction system.
dt Return the sampling time of the system, None for lti systems.
gain Gain of the ZerosPolesGain system.
num Numerator of the TransferFunction system.
poles Poles of the ZerosPolesGain system.
zeros Zeros of the ZerosPolesGain system.


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