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

Continuous-time linear time invariant system base class.


*system : arguments

The lti class can be instantiated with either 2, 3 or 4 arguments. The following gives the number of arguments and the corresponding continuous-time subclass that is created:

Each argument can be an array or a sequence.


lti instances do not exist directly. Instead, lti creates an instance of one of its subclasses: StateSpace, TransferFunction or ZerosPolesGain.

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 would be represented as [1, 3, 5]).

Changing the value of properties that are not directly part of the current system representation (such as the zeros of a StateSpace system) 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_zpk() before accessing/changing the zeros, poles or gain.


>>> from scipy import signal
>>> signal.lti(1, 2, 3, 4)
dt: None
>>> signal.lti([1, 2], [3, 4], 5)
array([1, 2]),
array([3, 4]),
dt: None
>>> signal.lti([3, 4], [1, 2])
array([ 3.,  4.]),
array([ 1.,  2.]),
dt: None


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.


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_discrete(dt[, method, alpha]) Return a discretized version of the current system.