`scipy.signal._filter_design:lp2bs_zpk`

source: /scipy/signal/_filter_design.py :3281

Signature

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

Parameters

z : array_like: Zeros of the analog filter transfer function.
p : array_like: Poles of the analog filter transfer function.
k : float: System gain of the analog filter transfer function.
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

z : ndarray: Zeros of the transformed band-stop filter transfer function.
p : ndarray: Poles of the transformed band-stop filter transfer function.
k : float: System gain 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_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 dev-arrayapi 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)

✗

Aliases

scipy.signal.lp2bs_zpk

Referenced by

This package

release:1.1.0-notes