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.

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.

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)