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# scipy.signal.TransferFunction

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

  Linear Time Invariant system class in transfer function form.

  Represents the system as the transfer function \(H(s)=\sum_i b[i] s^i / \sum_j a[j] s^i\), where \(a\) are elements of the numerator `num` and \(b\) are the elements of the denominator `den`.

  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` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`) 2: array_like: (numerator, denominator)

  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.

  Attributes

  `A` | A matrix of the `StateSpace` system.
  `B` | B matrix of the `StateSpace` system.
  `C` | C matrix of the `StateSpace` system.
  `D` | D matrix of the `StateSpace` system.
  `den` |
  `gain` | Gain of the `ZerosPolesGain` system.
  `num` |
  `poles` | Poles of the `ZerosPolesGain` system.
  `zeros` | Zeros of the `ZerosPolesGain` 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_ss`() | Convert system representation to `StateSpace`.
  `to_tf`() | Return a copy of the current `TransferFunction` system.
  `to_zpk`() | Convert system representation to `ZerosPolesGain`.