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# scipy.signal.lp2hp_zpk

scipy.signal.lp2hp_zpk(z, p, k, wo=1.0)

  Transform a lowpass filter prototype to a highpass filter.

  Return an analog high-pass filter with cutoff frequency wo 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 cutoff, as angular frequency (e.g., rad/s). Defaults to no change.

  Returns:
    z ndarray

      Zeros of the transformed high-pass filter transfer function.

    p ndarray

      Poles of the transformed high-pass filter transfer function.

    k float

      System gain of the transformed high-pass filter.

  See also

  `lp2lp_zpk`, `lp2bp_zpk`, `lp2bs_zpk`, `bilinear`
  `lp2hp`

  Notes

  This is derived from the s-plane substitution

  \[s \rightarrow \frac{\omega_0}{s}\]

  This maintains symmetry of the lowpass and highpass responses on a logarithmic scale.

  New in version 1.1.0.

  Examples

  Use the ‘zpk’ (Zero-Pole-Gain) representation of a lowpass filter to transform it to a highpass filter with a cutoff frequency wo.

      >>> from scipy.signal import lp2hp_zpk
      >>> z   = [ -2 + 3j ,  -0.5 - 0.8j ]
      >>> p   = [ -1      ,  -4          ]
      >>> k   = 10
      >>> wo  = 0.6
      >>> lp2hp_zpk(z, p, k, wo)
      (   array([-0.09230769-0.13846154j, -0.33707865+0.53932584j]),
          array([-0.6 , -0.15]),
          8.5)