# scipy.signal.freqresp

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

  Calculate the frequency response of a continuous-time system.

  Parameters:
    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.

  Returns:
    w 1D ndarray

      Frequency array [rad/s]

    H 1D ndarray

      Array of complex magnitude values

  Notes

  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]`).

  Examples

  Generating the Nyquist plot of a transfer function

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

  Construct the transfer function \(H(s) = \frac{5}{(s-1)^3}\):

      >>> 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")
      >>> plt.show()