scipy.signal.freqresp(system, w=None, n=10000)[source]

Calculate the frequency response of a continuous-time system.


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

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

  • 1 (instance of lti)
  • 2 (num, den)
  • 3 (zeros, poles, gain)
  • 4 (A, B, C, D)

w : array_like, optional

Array of frequencies (in rad/s). 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.


w : 1D ndarray

Frequency array [rad/s]

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. s^2 + 3s + 5 would be represented as [1, 3, 5]).


Generating the Nyquist plot of a transfer function

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

Transfer function: H(s) = 5 / (s-1)^3

>>> s1 = signal.ZerosPolesGain([], [1, 1, 1], [5])
>>> w, H = signal.freqresp(s1)
>>> plt.figure()
>>> plt.plot(H.real, H.imag, "b")
>>> plt.plot(H.real, -H.imag, "r")

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