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# scipy.signal.lp2bp_zpk

scipy.signal.lp2bp_zpk(z, p, k, wo=1.0, bw=1.0)

  Transform a lowpass filter prototype to a bandpass filter.

  Return an analog band-pass filter with center frequency wo and bandwidth 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 passband center, as angular frequency (e.g., rad/s). Defaults to no change.

    bw float

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

  Returns:
    z ndarray

      Zeros of the transformed band-pass filter transfer function.

    p ndarray

      Poles of the transformed band-pass filter transfer function.

    k float

      System gain of the transformed band-pass filter.

  See also

  `lp2lp_zpk`, `lp2hp_zpk`, `lp2bs_zpk`, `bilinear`
  `lp2bp`

  Notes

  This is derived from the s-plane substitution

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

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

  New in version 1.1.0.

  Examples

  Use the ‘zpk’ (Zero-Pole-Gain) representation of a lowpass filter to transform it to a bandpass filter with a center frequency wo and bandwidth bw.

      >>> from scipy.signal import lp2bp_zpk
      >>> z   = [ 5 + 2j ,  5 - 2j ]
      >>> p   = [ 7      ,  -16    ]
      >>> k   = 0.8
      >>> wo  = 0.62
      >>> bw  = 15
      >>> lp2bp_zpk(z, p, k, wo, bw)
      (   array([7.49955815e+01+3.00017676e+01j, 7.49955815e+01-3.00017676e+01j,
                 4.41850748e-03-1.76761126e-03j, 4.41850748e-03+1.76761126e-03j]),
          array([1.04996339e+02+0.j, -1.60167736e-03+0.j,  3.66108003e-03+0.j,
                 -2.39998398e+02+0.j]), 0.8)