scipy.signal.

lp2bs#

scipy.signal.lp2bs(b, a, wo=1.0, bw=1.0)[source]#

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:

barray_like: Numerator polynomial coefficients.
aarray_like: Denominator polynomial coefficients.
wofloat: Desired stopband center, as angular frequency (e.g., rad/s). Defaults to no change.
bwfloat: Desired stopband width, as angular frequency (e.g., rad/s). Defaults to 1.

Returns:

barray_like: Numerator polynomial coefficients of the transformed band-stop filter.
aarray_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.

Array API Standard Support

lp2bs 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, 1.5])
>>> 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('Amplitude [dB]')
>>> plt.legend()