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

Linear Time Invariant system class in transfer function form.

Represents the system as the transfer function \(H(s)=\sum_{i=0}^N b[N-i] s^i / \sum_{j=0}^M a[M-j] s^j\), where \(b\) are elements of the numerator num, \(a\) are elements of the denominator den, and N == len(b) - 1, M == len(a) - 1.


*system : arguments

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


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.


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.])


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.
gain Gain of the ZerosPolesGain system.
num Numerator of the TransferFunction system.
poles Poles of the ZerosPolesGain system.
zeros Zeros of the ZerosPolesGain system.


bode([w, n]) Calculate Bode magnitude and phase data of a continuous-time system.
freqresp([w, n]) Calculate the frequency response of a continuous-time system.
impulse([X0, T, N]) Return the impulse response of a continuous-time system.
output(U, T[, X0]) Return the response of a continuous-time system to input U.
step([X0, T, N]) Return the step response of a continuous-time 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.