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# scipy.signal.lp2bp

scipy.signal.lp2bp(b, a, 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, in transfer function (‘ba’) representation.

  Parameters:
    b array_like

      Numerator polynomial coefficients.

    a array_like

      Denominator polynomial coefficients.

    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:
    b array_like

      Numerator polynomial coefficients of the transformed band-pass filter.

    a array_like

      Denominator polynomial coefficients of the transformed band-pass filter.

  See also

  `lp2lp`, `lp2hp`, `lp2bs`, `bilinear`
  `lp2bp_zpk`

  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.

  Examples

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

      >>> lp = signal.lti([1.0], [1.0, 1.0])
      >>> bp = signal.lti(*signal.lp2bp(lp.num, lp.den))
      >>> w, mag_lp, p_lp = lp.bode()
      >>> w, mag_bp, p_bp = bp.bode(w)

      >>> plt.plot(w, mag_lp, label='Lowpass')
      >>> plt.plot(w, mag_bp, label='Bandpass')
      >>> plt.semilogx()
      >>> plt.grid(True)
      >>> plt.xlabel('Frequency [rad/s]')
      >>> plt.ylabel('Magnitude [dB]')
      >>> plt.legend()