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# scipy.signal.freqs_zpk

`scipy.signal.``freqs_zpk`(z, p, k, worN=None)

  Compute frequency response of analog filter.

  Given the zeros z, poles p, and gain k of a filter, compute its frequency response:

                 (jw-z[0]) * (jw-z[1]) * ... * (jw-z[-1])
      H(w) = k * ----------------------------------------
                 (jw-p[0]) * (jw-p[1]) * ... * (jw-p[-1])

  Parameters: | z : array_like Zeroes of a linear filter p : array_like Poles of a linear filter k : scalar Gain of a linear filter worN : {None, int, array_like}, optional If None, then compute at 200 frequencies around the interesting parts of the response curve (determined by pole-zero locations). If a single integer, then compute at that many frequencies. Otherwise, compute the response at the angular frequencies (e.g. rad/s) given in worN.
  Returns: | w : ndarray The angular frequencies at which h was computed. h : ndarray The frequency response.

  See also

  `freqs`
    Compute the frequency response of an analog filter in TF form
  `freqz`
    Compute the frequency response of a digital filter in TF form
  `freqz_zpk`
    Compute the frequency response of a digital filter in ZPK form

  Notes

  Examples

      >>> from scipy.signal import freqs_zpk, iirfilter

      >>> z, p, k = iirfilter(4, [1, 10], 1, 60, analog=True, ftype='cheby1',
      ...                     output='zpk')

      >>> w, h = freqs_zpk(z, p, k, worN=np.logspace(-1, 2, 1000))

      >>> import matplotlib.pyplot as plt
      >>> plt.semilogx(w, 20 * np.log10(abs(h)))
      >>> plt.xlabel('Frequency')
      >>> plt.ylabel('Amplitude response [dB]')
      >>> plt.grid()
      >>> plt.show()

  (Source code)