scipy.signal.dlsim(system, u, t=None, x0=None)[source]

Simulate output of a discrete-time linear system.


system : tuple of array_like

A tuple describing the system. The following gives the number of elements in the tuple and the interpretation:

  • 3: (num, den, dt)
  • 4: (zeros, poles, gain, dt)
  • 5: (A, B, C, D, dt)

u : array_like

An input array describing the input at each time t (interpolation is assumed between given times). If there are multiple inputs, then each column of the rank-2 array represents an input.

t : array_like, optional

The time steps at which the input is defined. If t is given, it must be the same length as u, and the final value in t determines the number of steps returned in the output.

x0 : array_like, optional

The initial conditions on the state vector (zero by default).


tout : ndarray

Time values for the output, as a 1-D array.

yout : ndarray

System response, as a 1-D array.

xout : ndarray, optional

Time-evolution of the state-vector. Only generated if the input is a state-space systems.


A simple integrator transfer function with a discrete time step of 1.0 could be implemented as:

>>> from scipy import signal
>>> tf = ([1.0,], [1.0, -1.0], 1.0)
>>> t_in = [0.0, 1.0, 2.0, 3.0]
>>> u = np.asarray([0.0, 0.0, 1.0, 1.0])
>>> t_out, y = signal.dlsim(tf, u, t=t_in)
>>> y.T
array([[ 0.,  0.,  0.,  1.]])

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