scipy.signal.dfreqresp(system, w=None, n=10000, whole=False)[source]

Calculate the frequency response of a discrete-time system.


system : an instance of the dlti class or a tuple describing the system.

The following gives the number of elements in the tuple and the interpretation:

  • 1 (instance of dlti)
  • 2 (numerator, denominator, dt)
  • 3 (zeros, poles, gain, dt)
  • 4 (A, B, C, D, dt)

w : array_like, optional

Array of frequencies (in radians/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.

whole : bool, optional

Normally, if ‘w’ is not given, frequencies are computed from 0 to the Nyquist frequency, pi radians/sample (upper-half of unit-circle). If whole is True, compute frequencies from 0 to 2*pi radians/sample.


w : 1D ndarray

Frequency array [radians/sample]

H : 1D ndarray

Array of complex magnitude values


If (num, den) 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]).

New in version 0.18.0.


Generating the Nyquist plot of a transfer function

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

Transfer function: H(z) = 1 / (z^2 + 2z + 3)

>>> sys = signal.TransferFunction([1], [1, 2, 3], dt=0.05)
>>> w, H = signal.dfreqresp(sys)
>>> plt.figure()
>>> plt.plot(H.real, H.imag, "b")
>>> plt.plot(H.real, -H.imag, "r")

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