scipy.signal.

lp2bs_zpk#

scipy.signal.lp2bs_zpk(z, p, k, 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 stopband width bw from an analog low-pass filter prototype with unity cutoff frequency, using zeros, poles, and gain (‘zpk’) representation.

Parameters:

zarray_like: Zeros of the analog filter transfer function.
parray_like: Poles of the analog filter transfer function.
kfloat: System gain of the analog filter transfer function.
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:

zndarray: Zeros of the transformed band-stop filter transfer function.
pndarray: Poles of the transformed band-stop filter transfer function.
kfloat: System gain of the transformed band-stop filter.

See also

lp2lp_zpk, lp2hp_zpk, lp2bp_zpk, bilinear
lp2bs

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.

Added in version 1.1.0.

Array API Standard Support

lp2bs_zpk 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 Support for the array API standard for more information.

Examples

Transform a low-pass filter represented in ‘zpk’ (Zero-Pole-Gain) form into a bandstop filter represented in ‘zpk’ form, with a center frequency wo and bandwidth bw.

>>> from scipy.signal import lp2bs_zpk
>>> z   = [             ]
>>> p   = [ 0.7 ,    -1 ]
>>> k   = 9
>>> wo  = 0.5
>>> bw  = 10
>>> lp2bs_zpk(z, p, k, wo, bw)
(   array([0.+0.5j, 0.+0.5j, 0.-0.5j, 0.-0.5j]),
    array([14.2681928 +0.j, -0.02506281+0.j,  0.01752149+0.j, -9.97493719+0.j]),
    -12.857142857142858)