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 :None:None:`gain`, $z$ are the zeros and $p$ are the :None:None:`poles`. ZerosPolesGain systems inherit additional functionality from the lti , respectively the dlti classes, depending on which system representation is used.

Notes

Changing the value of properties that are not part of the ZerosPolesGain system representation (such as the :None:None:`A`, :None:None:`B`, :None:None:`C`, :None:None:`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.

Parameters

*system : arguments

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:None:`None` (continuous-time). Must be specified as a keyword argument, for example, dt=0.1 .

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

See Also

StateSpace

TransferFunction

dlti

lti

zpk2sos

zpk2ss

zpk2tf

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
)

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._ltisys.TransferFunctionContinuous scipy.signal._ltisys.ZerosPolesGainContinuous.to_discrete scipy.signal._ltisys.TransferFunctionDiscrete scipy.signal._ltisys.LinearTimeInvariant._as_zpk scipy.signal._ltisys.dlti scipy.signal._ltisys.StateSpace scipy.signal._ltisys.StateSpace.to_zpk scipy.signal._ltisys.lti scipy.signal._ltisys.ZerosPolesGainDiscrete scipy.signal._ltisys.freqresp scipy.signal._ltisys.ZerosPolesGainContinuous scipy.signal._ltisys.ZerosPolesGain._copy scipy.signal._ltisys.StateSpaceContinuous scipy.signal._ltisys.TransferFunction.to_zpk scipy.signal._ltisys.ZerosPolesGain scipy.signal._ltisys.TransferFunction scipy.signal._ltisys.StateSpaceDiscrete scipy.signal._ltisys.ZerosPolesGain.__repr__

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