scipy.signal.TransferFunction¶

class
scipy.signal.
TransferFunction
(*system, **kwargs)[source]¶ Linear Time Invariant system class in transfer function form.
Represents the system as the continuoustime transfer function \(H(s)=\sum_{i=0}^N b[Ni] s^i / \sum_{j=0}^M a[Mj] s^j\) or the discretetime transfer function \(H(s)=\sum_{i=0}^N b[Ni] z^i / \sum_{j=0}^M a[Mj] z^j\), where \(b\) are elements of the numerator
num
, \(a\) are elements of the denominatorden
, andN == len(b)  1
,M == len(a)  1
.TransferFunction
systems inherit additional functionality from thelti
, respectively thedlti
classes, depending on which system representation is used.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
ordlti
system: (StateSpace
,TransferFunction
orZerosPolesGain
)  2: array_like: (numerator, denominator)
dt: float, optional
Sampling time [s] of the discretetime systems. Defaults to None (continuoustime). Must be specified as a keyword argument, for example,
dt=0.1
.See also
ZerosPolesGain
,StateSpace
,lti
,dlti
,tf2ss
,tf2zpk
,tf2sos
Notes
Changing the value of properties that are not part of the
TransferFunction
system representation (such as theA
,B
,C
,D
statespace matrices) is very inefficient and may lead to numerical inaccuracies. It is better to convert to the specific system representation first. For example, callsys = 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
orz^2 + 3z + 5
would be represented as[1, 3, 5]
)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 )
Contruct 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) TransferFunctionDiscrete( array([ 1., 3., 3.]), array([ 1., 2., 1.]), dt: 0.1 )
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.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. Methods
to_ss
()Convert system representation to StateSpace
.to_tf
()Return a copy of the current TransferFunction
system.to_zpk
()Convert system representation to ZerosPolesGain
. 1: