scipy.signal.

dlsim#

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

Simulate output of a discrete-time linear system.

Parameters:
systemdlti | tuple

An instance of the LTI class dlti or a tuple describing the system. The number of elements in the tuple determine the interpretation. I.e.:

  • system: Instance of LTI class dlti. Note that derived instances, such as instances of TransferFunction, ZerosPolesGain, or StateSpace, are allowed as well.

  • (num, den, dt): Rational polynomial as described in TransferFunction. The coefficients of the polynomials should be specified in descending exponent order, e.g., z² + 3z + 5 would be represented as [1, 3, 5].

  • (zeros, poles, gain, dt): Zeros, poles, gain form as described in ZerosPolesGain.

  • (A, B, C, D, dt): State-space form as described in StateSpace.

uarray_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.

tarray_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.

x0array_like, optional

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

Returns:
toutndarray

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

youtndarray

System response, as a 1-D array.

xoutndarray, optional

Time-evolution of the state-vector. Only generated if the input is a StateSpace system.

See also

lsim, dstep, dimpulse, cont2discrete

Notes

Array API Standard Support

dlsim has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library

CPU

GPU

NumPy

✅

n/a

CuPy

n/a

⛔

PyTorch

⛔

⛔

JAX

⛔

⛔

Dask

⛔

n/a

See Support for the array API standard for more information.

Examples

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

>>> import numpy as np
>>> 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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