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scipy.signal.

# lp2hp

scipy.signal.lp2hp(b, a, 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, in transfer function (‘ba’) representation.

  Parameters:
    b array_like

      Numerator polynomial coefficients.

    a array_like

      Denominator polynomial coefficients.

    wo float

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

  Returns:
    b array_like

      Numerator polynomial coefficients of the transformed high-pass filter.

    a array_like

      Denominator polynomial coefficients of the transformed high-pass filter.

  See also

  `lp2lp`, `lp2bp`, `lp2bs`, `bilinear`
  `lp2hp_zpk`

  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.

  Array API Standard Support

  `lp2hp` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ⛔ | ⛔
  Dask | ⚠️ computes graph | n/a

  > See Support for the array API standard for more information.

  Examples

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

      >>> lp = signal.lti([1.0], [1.0, 1.0])
      >>> hp = signal.lti(*signal.lp2hp(lp.num, lp.den))
      >>> w, mag_lp, p_lp = lp.bode()
      >>> w, mag_hp, p_hp = hp.bode(w)

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