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# scipy.signal.TransferFunction

class `scipy.signal.``TransferFunction`(*system, **kwargs)

  Linear Time Invariant system class in transfer function form.

  Represents the system as the continuous-time transfer function \(H(s)=\sum_{i=0}^N b[N-i] s^i / \sum_{j=0}^M a[M-j] s^j\) or the discrete-time transfer function \(H(s)=\sum_{i=0}^N b[N-i] z^i / \sum_{j=0}^M a[M-j] z^j\), where \(b\) are elements of the numerator `num`, \(a\) are elements of the denominator `den`, and `N == len(b) - 1`, `M == len(a) - 1`. `TransferFunction` systems inherit additional functionality from the `lti`, respectively the `dlti` classes, depending on which system representation is used.

  Parameters: | *system: arguments The `TransferFunction` class can be instantiated with 1 or 2 arguments. The following gives the number of input arguments and their interpretation: 1: `lti` or `dlti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`) 2: array_like: (numerator, denominator) 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

  `ZerosPolesGain`, `StateSpace`, `lti`, `dlti`, `tf2ss`, `tf2zpk`, `tf2sos`

  Notes

  Changing the value of properties that are not part of the `TransferFunction` 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.

  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` or `z^2 + 3z + 5` would be represented as `[1, 3, 5]`)

  Examples

  Construct the transfer function:

  \[H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}\]

      >>> from scipy import signal

      >>> num = [1, 3, 3]
      >>> den = [1, 2, 1]

      >>> signal.TransferFunction(num, den)
      TransferFunctionContinuous(
      array([ 1.,  3.,  3.]),
      array([ 1.,  2.,  1.]),
      dt: None
      )

  Contruct the transfer function with a sampling time of 0.1 seconds:

  \[H(z) = \frac{z^2 + 3z + 3}{z^2 + 2z + 1}\]

      >>> signal.TransferFunction(num, den, dt=0.1)
      TransferFunctionDiscrete(
      array([ 1.,  3.,  3.]),
      array([ 1.,  2.,  1.]),
      dt: 0.1
      )

  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

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