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Module « scipy.signal »

Fonction dbode - module scipy.signal

Signature de la fonction dbode

def dbode(system, w=None, n=100) 

Description

help(scipy.signal.dbode)

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

Parameters
----------
system :
    An instance of the LTI class `dlti` or a tuple describing the system.
    The number of elements in the tuple determine the interpretation, i.e.:

    1. ``(sys_dlti)``:  Instance of LTI class `dlti`. Note that derived instances,
       such as instances of `TransferFunction`, `ZerosPolesGain`, or `StateSpace`,
       are allowed as well.
    2. ``(num, den, dt)``: Rational polynomial as described in `TransferFunction`.
       The coefficients of the polynomials should be specified in descending
       exponent order,  e.g., z² + 3z + 5 would be represented as ``[1, 3, 5]``.
    3. ``(zeros, poles, gain, dt)``:  Zeros, poles, gain form as described
       in `ZerosPolesGain`.
    4. ``(A, B, C, D, dt)``: State-space form as described in `StateSpace`.

w : array_like, optional
    Array of frequencies normalized to the Nyquist frequency being π, i.e.,
    having unit radiant / sample. Magnitude and phase data is calculated for every
    value in this array. If not given, a reasonable set will be calculated.
n : int, optional
    Number of frequency points to compute if `w` is not given. The `n`
    frequencies are logarithmically spaced in an interval chosen to
    include the influence of the poles and zeros of the system.

Returns
-------
w : 1D ndarray
    Array of frequencies normalized to the Nyquist frequency being ``np.pi/dt``
    with ``dt`` being the sampling interval of the `system` parameter.
    The unit is rad/s assuming ``dt`` is in seconds.
mag : 1D ndarray
    Magnitude array in dB
phase : 1D ndarray
    Phase array in degrees

Notes
-----
This function is a convenience wrapper around `dfreqresp` for extracting
magnitude and phase from the calculated complex-valued amplitude of the
frequency response.

.. versionadded:: 0.18.0

See Also
--------
dfreqresp, dlti, TransferFunction, ZerosPolesGain, StateSpace


Examples
--------
The following example shows how to create a Bode plot of a 5-th order
Butterworth lowpass filter with a corner frequency of 100 Hz:

>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from scipy import signal
...
>>> T = 1e-4  # sampling interval in s
>>> f_c, o = 1e2, 5  # corner frequency in Hz (i.e., -3 dB value) and filter order
>>> bb, aa = signal.butter(o, f_c, 'lowpass', fs=1/T)
...
>>> w, mag, phase = signal.dbode((bb, aa, T))
>>> w /= 2*np.pi  # convert unit of frequency into Hertz
...
>>> fg, (ax0, ax1) = plt.subplots(2, 1, sharex='all', figsize=(5, 4),
...                               tight_layout=True)
>>> ax0.set_title("Bode Plot of Butterworth Lowpass Filter " +
...               rf"($f_c={f_c:g}\,$Hz, order={o})")
>>> ax0.set_ylabel(r"Magnitude in dB")
>>> ax1.set(ylabel=r"Phase in Degrees",
...         xlabel="Frequency $f$ in Hertz", xlim=(w[1], w[-1]))
>>> ax0.semilogx(w, mag, 'C0-', label=r"$20\,\log_{10}|G(f)|$")  # Magnitude plot
>>> ax1.semilogx(w, phase, 'C1-', label=r"$\angle G(f)$")  # Phase plot
...
>>> for ax_ in (ax0, ax1):
...     ax_.axvline(f_c, color='m', alpha=0.25, label=rf"${f_c=:g}\,$Hz")
...     ax_.grid(which='both', axis='x')  # plot major & minor vertical grid lines
...     ax_.grid(which='major', axis='y')
...     ax_.legend()
>>> plt.show()

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