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

Linear Time Invariant system class in transfer function form.

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 num, \(a\) are elements of the denominator 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.


*system: arguments

The TransferFunction class can be instantiated with 1 or 2 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 TransferFunction 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.

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])


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)
array([ 1.,  3.,  3.]),
array([ 1.,  2.,  1.]),
dt: None

Contruct the transfer function with a sampling time of 0.5 seconds:

\[H(z) = \frac{z^2 + 3z + 3}{z^2 + 2z + 1}\]
>>> signal.TransferFunction(num, den, dt=0.1)
array([ 1.,  3.,  3.]),
array([ 1.,  2.,  1.]),
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 system.
zeros Zeros of the system.


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