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# scipy.signal.freqz

`scipy.signal.``freqz`(b, a=1, worN=None, whole=0, plot=None)

  Compute the frequency response of a digital filter.

  Given the numerator `b` and denominator `a` of a digital filter compute its frequency response:

                jw               -jw            -jmw
         jw  B(e)    b[0] + b[1]e + .... + b[m]e
      H(e) = ---- = ------------------------------------
                jw               -jw            -jnw
             A(e)    a[0] + a[1]e + .... + a[n]e

  Parameters : | b : ndarray numerator of a linear filter a : ndarray denominator of a linear filter worN : {None, int}, optional If None, then compute at 512 frequencies around the unit circle. If a single integer, the compute at that many frequencies. Otherwise, compute the response at frequencies given in worN whole : bool, optional Normally, frequencies are computed from 0 to pi (upper-half of unit-circle. If whole is False, compute frequencies from 0 to 2*pi. plot : callable A callable that takes two arguments. If given, the return parameters w and h are passed to plot. Useful for plotting the frequency response inside freqz.
  Returns : | w : ndarray The frequencies at which h was computed. h : ndarray The frequency response.

  Notes

  Using Matplotlib’s “plot” function as the callable for plot produces unexpected results, this plots the real part of the complex transfer function, not the magnitude.

  Examples

      >>> b = firwin(80, 0.5, window=('kaiser', 8))
      >>> h, w = freqz(b)

      >>> import matplotlib.pyplot as plt
      >>> fig = plt.figure()
      >>> plt.title('Digital filter frequency response')
      >>> ax1 = fig.add_subplot(111)

      >>> plt.semilogy(h, np.abs(w), 'b')
      >>> plt.ylabel('Amplitude (dB)', color='b')
      >>> plt.xlabel('Frequency (rad/sample)')
      >>> plt.grid()
      >>> plt.legend()

      >>> ax2 = ax1.twinx()
      >>> angles = np.unwrap(np.angle(w))
      >>> plt.plot(h, angles, 'g')
      >>> plt.ylabel('Angle (radians)', color='g')
      >>> plt.show()

  (Source code)

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