`scipy.signal._ltisys:dbode`

source: build-install/usr/lib/python3.14/site-packages/scipy/signal/_ltisys.py:3758

Signature

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

Summary

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

Parameters

system : dlti | tuple

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.:

system: Instance of LTI class dlti. Note that derived instances, such as instances of TransferFunction, ZerosPolesGain, or StateSpace, are allowed as well.
(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].
(zeros, poles, gain, dt): Zeros, poles, gain form as described in ZerosPolesGain.
(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.

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()

✗

<matplotlib.lines.Line2D object at 0x7f3f68825550>
<matplotlib.legend.Legend object at 0x7f3f688256a0>
<matplotlib.lines.Line2D object at 0x7f3f68825d30>
<matplotlib.legend.Legend object at 0x7f3f68825e80>

plt.show()

✓

Aliases

scipy.signal.dbode