# scipy.signal.dlti

class scipy.signal.dlti(*system, **kwargs)

  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:

      > - 2: `TransferFunction`: (numerator, denominator)

      > - 3: `ZerosPolesGain`: (zeros, poles, gain)

      > - 4: `StateSpace`: (A, B, C, D)

      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`.

  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]`).

  New in version 0.18.0.

  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
      )

  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.