Represents the system as the continuous-time transfer function $H(s)=\sum_{i=0}^N b[N-i] s^i / \sum_{j=0}^M a[M-j] s^j$ or the discrete-time transfer function $H(s)=\sum_{i=0}^N b[N-i] z^i / \sum_{j=0}^M a[M-j] z^j$ , where $b$ are elements of the numerator :None:None:`num`, $a$ are elements of the denominator :None:None:`den`, and N == len(b) - 1 , M == len(a) - 1 . TransferFunction 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 TransferFunction 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.

If (numerator, denominator) is passed in for *system , coefficients for both the numerator and denominator should be specified in descending exponent order (e.g. s^2 + 3s + 5 or z^2 + 3z + 5 would be represented as [1, 3, 5] )

Parameters

*system: arguments :

The TransferFunction class can be instantiated with 1 or 2 arguments. The following gives the number of input arguments and their interpretation:

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

• 2: array_like: (numerator, denominator)

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 transfer function form.

See Also

StateSpace

ZerosPolesGain

dlti

lti

tf2sos

tf2ss

tf2zpk

Examples

Construct the transfer function $H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}$ :

>>> from scipy import signal

>>> num = [1, 3, 3]
... den = [1, 2, 1]

>>> signal.TransferFunction(num, den)
TransferFunctionContinuous(
array([1., 3., 3.]),
array([1., 2., 1.]),
dt: None
)

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

>>> signal.TransferFunction(num, den, dt=0.1)
TransferFunctionDiscrete(
array([1., 3., 3.]),
array([1., 2., 1.]),
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.to_discrete scipy.signal._ltisys.dlti scipy.signal._ltisys.lti.bode scipy.signal._ltisys.dlti.bode scipy.signal._ltisys.StateSpaceDiscrete scipy.signal._ltisys.TransferFunctionContinuous scipy.signal._ltisys.StateSpace scipy.signal._ltisys.lti scipy.signal._ltisys.TransferFunction scipy.signal._ltisys.TransferFunction.to_tf scipy.signal._ltisys.TransferFunctionDiscrete scipy.signal._ltisys.LinearTimeInvariant._as_tf scipy.signal._ltisys.bode scipy.signal._ltisys.StateSpaceContinuous scipy.signal._ltisys.TransferFunction._copy scipy.signal._ltisys.StateSpace.to_tf scipy.signal._ltisys.ZerosPolesGainDiscrete scipy.signal._ltisys.ZerosPolesGainContinuous scipy.signal._ltisys.ZerosPolesGain.to_tf scipy.signal._ltisys.dfreqresp scipy.signal._ltisys.ZerosPolesGain scipy.signal._ltisys.dbode

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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