`scipy.signal._filter_design:lp2bs`

source: /scipy/signal/_filter_design.py:2236

Signature

def lp2bs(b, a, wo = 1.0, bw = 1.0)

Summary

Transform a lowpass filter prototype to a bandstop filter.

Extended Summary

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, shape (M,): Numerator polynomial coefficients. Must be 1-D.
a : array_like, shape (N,): Denominator polynomial coefficients. Must be 1-D.
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.

Notes

This is derived from the s-plane substitution

s \to \frac{s \cdot BW}{s ^{2} + ω _{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                   ⚠️ no JIT             ⛔                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi 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()

✗

<matplotlib.legend.Legend object at 0x7fa8e7e07230>

Aliases

scipy.signal.lp2bs