# scipy.signal.ZerosPolesGain

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

  Linear Time Invariant system class in zeros, poles, gain form.

  Represents the system as the continuous- or discrete-time transfer function \(H(s)=k \prod_i (s - z[i]) / \prod_j (s - p[j])\), where \(k\) is the `gain`, \(z\) are the `zeros` and \(p\) are the `poles`. `ZerosPolesGain` systems inherit additional functionality from the `lti`, respectively the `dlti` classes, depending on which system representation is used.

  Parameters:
    *system arguments

      The `ZerosPolesGain` class can be instantiated with 1 or 3 arguments. The following gives the number of input arguments and their interpretation:

      > - 1: `lti` or `dlti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)

      > - 3: array_like: (zeros, poles, gain)

    dt: float, optional

      Sampling time [s] of the discrete-time systems. Defaults to None (continuous-time). Must be specified as a keyword argument, for example, `dt=0.1`.

  See also

  `TransferFunction`, `StateSpace`, `lti`, `dlti`
  `zpk2ss`, `zpk2tf`, `zpk2sos`

  Notes

  Changing the value of properties that are not part of the `ZerosPolesGain` system representation (such as the A, B, C, D state-space matrices) 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_ss()` before accessing/changing the A, B, C, D system matrices.

  Examples

  Construct the transfer function \(H(s) = \frac{5(s - 1)(s - 2)}{(s - 3)(s - 4)}\):

      >>> from scipy import signal

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

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

  Attributes:
    `dt`

      Return the sampling time of the system, None for `lti` systems.

    `gain`

      Gain of the `ZerosPolesGain` system.

    `poles`

      Poles of the `ZerosPolesGain` system.

    `zeros`

      Zeros of the `ZerosPolesGain` system.

  Methods

  `to_ss`() | Convert system representation to `StateSpace`.
  `to_tf`() | Convert system representation to `TransferFunction`.
  `to_zpk`() | Return a copy of the current 'ZerosPolesGain' system.