scipy.signal.TransferFunction

class scipy.signal.TransferFunction(*system)

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.

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 system: (StateSpace, TransferFunction or ZerosPolesGain)
• 2: array_like: (numerator, denominator)

See also

ZerosPolesGain, StateSpace, lti, tf2ss, tf2zpk, tf2sos

Notes

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.

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)
TransferFunction(
array([ 1.,  3.,  3.]),
array([ 1.,  2.,  1.])
)

Attributes

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.

Methods

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.