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# scipy.signal.lp2bs_zpk

scipy.signal.lp2bs_zpk(z, p, k, wo=1.0, bw=1.0)

  Transform a lowpass filter prototype to a bandstop filter.

  Return an analog band-stop filter with center frequency wo and stopband width bw from an analog low-pass filter prototype with unity cutoff frequency, using zeros, poles, and gain (‘zpk’) representation.

  Parameters:
    z array_like

      Zeros of the analog filter transfer function.

    p array_like

      Poles of the analog filter transfer function.

    k float

      System gain of the analog filter transfer function.

    wo float

      Desired stopband center, as angular frequency (e.g., rad/s). Defaults to no change.

    bw float

      Desired stopband width, as angular frequency (e.g., rad/s). Defaults to 1.

  Returns:
    z ndarray

      Zeros of the transformed band-stop filter transfer function.

    p ndarray

      Poles of the transformed band-stop filter transfer function.

    k float

      System gain of the transformed band-stop filter.

  See also

  `lp2lp_zpk`, `lp2hp_zpk`, `lp2bp_zpk`, `bilinear`
  `lp2bs`

  Notes

  This is derived from the s-plane substitution

  \[s \rightarrow \frac{s \cdot \mathrm{BW}}{s^2 + {\omega_0}^2}\]

  This is the “wideband” transformation, producing a stopband with geometric (log frequency) symmetry about wo.

  New in version 1.1.0.

  Examples

  Transform a low-pass filter represented in ‘zpk’ (Zero-Pole-Gain) form into a bandstop filter represented in ‘zpk’ form, with a center frequency wo and bandwidth bw.

      >>> from scipy.signal import lp2bs_zpk
      >>> z   = [             ]
      >>> p   = [ 0.7 ,    -1 ]
      >>> k   = 9
      >>> wo  = 0.5
      >>> bw  = 10
      >>> lp2bs_zpk(z, p, k, wo, bw)
      (   array([0.+0.5j, 0.+0.5j, 0.-0.5j, 0.-0.5j]),
          array([14.2681928 +0.j, -0.02506281+0.j,  0.01752149+0.j, -9.97493719+0.j]),
          -12.857142857142858)