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# scipy.signal.dfreqresp

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

  Calculate the frequency response of a discrete-time system.

  Parameters:
    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.

  Returns:
    w 1D ndarray

      Frequency array [radians/sample]

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

  New in version 0.18.0.

  Examples

  Generating the Nyquist plot of a transfer function

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

  Construct the transfer function \(H(z) = \frac{1}{z^2 + 2z + 3}\) with a sampling time of 0.05 seconds:

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