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

Construct the transfer function with a sampling time of 0.1 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

Denominator of the TransferFunction system.


Return the sampling time of the system, None for lti systems.


Numerator of the TransferFunction system.


Poles of the system.


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.