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# scipy.signal.lp2bs

scipy.signal.lp2bs(b, a, 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 bandwidth bw from an analog low-pass filter prototype with unity cutoff frequency, in transfer function (‘ba’) representation.

  Parameters:
    b array_like

      Numerator polynomial coefficients.

    a array_like

      Denominator polynomial coefficients.

    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:
    b array_like

      Numerator polynomial coefficients of the transformed band-stop filter.

    a array_like

      Denominator polynomial coefficients of the transformed band-stop filter.

  See also

  `lp2lp`, `lp2hp`, `lp2bp`, `bilinear`
  `lp2bs_zpk`

  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.

  Examples

      >>> from scipy import signal
      >>> import matplotlib.pyplot as plt

      >>> lp = signal.lti([1.0], [1.0, 1.5])
      >>> bs = signal.lti(*signal.lp2bs(lp.num, lp.den))
      >>> w, mag_lp, p_lp = lp.bode()
      >>> w, mag_bs, p_bs = bs.bode(w)
      >>> plt.plot(w, mag_lp, label='Lowpass')
      >>> plt.plot(w, mag_bs, label='Bandstop')
      >>> plt.semilogx()
      >>> plt.grid(True)
      >>> plt.xlabel('Frequency [rad/s]')
      >>> plt.ylabel('Magnitude [dB]')
      >>> plt.legend()