scipy.signal.

dlti#

class scipy.signal.dlti(*system, **kwargs)[source]#

Discrete-time linear time invariant system base class.

Parameters:
*system: arguments

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

Each argument can be an array or a sequence.

dt: float, optional

Sampling time [s] of the discrete-time systems. Defaults to True (unspecified sampling time). Must be specified as a keyword argument, for example, dt=0.1.

Attributes:
dt

Return the sampling time of the system.

poles

Poles of the system.

zeros

Zeros of the system.

Methods

bode([w, n])

Calculate Bode magnitude and phase data of a discrete-time system.

freqresp([w, n, whole])

Calculate the frequency response of a discrete-time system.

impulse([x0, t, n])

Return the impulse response of the discrete-time dlti system.

output(u, t[, x0])

Return the response of the discrete-time system to input u.

step([x0, t, n])

Return the step response of the discrete-time dlti system.

See also

ZerosPolesGain, StateSpace, TransferFunction, lti

Notes

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

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.

If (numerator, denominator) is passed in for *system, coefficients for both the numerator and denominator should be specified in descending exponent order (e.g., z^2 + 3z + 5 would be represented as [1, 3, 5]).

Added in version 0.18.0.

Array API Standard Support

dlti 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

>>> from scipy import signal

>>> signal.dlti(1, 2, 3, 4)
StateSpaceDiscrete(
array([[1]]),
array([[2]]),
array([[3]]),
array([[4]]),
dt: True
)

>>> signal.dlti(1, 2, 3, 4, dt=0.1)
StateSpaceDiscrete(
array([[1]]),
array([[2]]),
array([[3]]),
array([[4]]),
dt: 0.1
)

Construct the transfer function \(H(z) = \frac{5(z - 1)(z - 2)}{(z - 3)(z - 4)}\) with a sampling time of 0.1 seconds:

>>> signal.dlti([1, 2], [3, 4], 5, dt=0.1)
ZerosPolesGainDiscrete(
array([1, 2]),
array([3, 4]),
5,
dt: 0.1
)

Construct the transfer function \(H(z) = \frac{3z + 4}{1z + 2}\) with a sampling time of 0.1 seconds:

>>> signal.dlti([3, 4], [1, 2], dt=0.1)
TransferFunctionDiscrete(
array([3., 4.]),
array([1., 2.]),
dt: 0.1
)
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