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# scipy.signal.lti

class `scipy.signal.``lti`(*system)

  Continuous-time linear time invariant system base class.

  Parameters: | *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: 2: `TransferFunction`: (numerator, denominator) 3: `ZerosPolesGain`: (zeros, poles, gain) 4: `StateSpace`: (A, B, C, D) Each argument can be an array or a sequence.

  See also

  `ZerosPolesGain`, `StateSpace`, `TransferFunction`, `dlti`

  Notes

  `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.

  Examples

      >>> from scipy import signal

      >>> signal.lti(1, 2, 3, 4)
      StateSpaceContinuous(
      array([[1]]),
      array([[2]]),
      array([[3]]),
      array([[4]]),
      dt: None
      )

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

      >>> signal.lti([3, 4], [1, 2])
      TransferFunctionContinuous(
      array([ 3.,  4.]),
      array([ 1.,  2.]),
      dt: None
      )

  Attributes

  `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.

  Methods

  `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.