package scipy

Discrete-time Linear Time Invariant system in transfer function form.

Represents the system as the transfer function :math:`H(z)=\sum_=0^N bN-i z^i / \sum_j=0^M aM-j z^j`, where :math:`b` are elements of the numerator `num`, :math:`a` are elements of the denominator `den`, and ``N == len(b) - 1``, ``M == len(a) - 1``. Discrete-time `TransferFunction` systems inherit additional functionality from the `dlti` class.

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

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``).

Examples -------- Construct the transfer function with a sampling time of 0.5 seconds:

.. math:: H(z) = \fracz^2 + 3z + 3z^2 + 2z + 1

>>> from scipy import signal

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

>>> signal.TransferFunction(num, den, 0.5) TransferFunctionDiscrete( array( 1., 3., 3.), array( 1., 2., 1.), dt: 0.5 )

Calculate Bode magnitude and phase data of a discrete-time system.

Returns a 3-tuple containing arrays of frequencies rad/s, magnitude dB and phase deg. See `dbode` for details.

Examples -------- >>> from scipy import signal >>> import matplotlib.pyplot as plt

Transfer function: H(z) = 1 / (z^2 + 2z + 3) with sampling time 0.5s

>>> sys = signal.TransferFunction(1, 1, 2, 3, dt=0.5)

Equivalent: signal.dbode(sys)

>>> w, mag, phase = sys.bode()

>>> plt.figure() >>> plt.semilogx(w, mag) # Bode magnitude plot >>> plt.figure() >>> plt.semilogx(w, phase) # Bode phase plot >>> plt.show()

Calculate the frequency response of a discrete-time system.

Returns a 2-tuple containing arrays of frequencies rad/s and complex magnitude. See `dfreqresp` for details.

Return the impulse response of the discrete-time `dlti` system. See `dimpulse` for details.

Return the response of the discrete-time system to input `u`. See `dlsim` for details.

Return the step response of the discrete-time `dlti` system. See `dstep` for details.

Convert system representation to `StateSpace`.

Returns ------- sys : instance of `StateSpace` State space model of the current system

Return a copy of the current `TransferFunction` system.

Returns ------- sys : instance of `TransferFunction` The current system (copy)

Convert system representation to `ZerosPolesGain`.

Returns ------- sys : instance of `ZerosPolesGain` Zeros, poles, gain representation of the current system

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.