scipy.signal.

lp2bp_zpk#

scipy.signal.lp2bp_zpk(z, p, k, wo=1.0, bw=1.0)[source]#

Transform a lowpass filter prototype to a bandpass filter.

Return an analog band-pass filter with center frequency wo and bandwidth 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 passband center, as angular frequency (e.g., rad/s). Defaults to no change.
bwfloat: Desired passband width, as angular frequency (e.g., rad/s). Defaults to 1.

Returns:

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

See also

lp2lp_zpk, lp2hp_zpk, lp2bs_zpk, bilinear
lp2bp

Notes

This is derived from the s-plane substitution

\[s \rightarrow \frac{s^2 + {\omega_0}^2}{s \cdot \mathrm{BW}}\]

This is the “wideband” transformation, producing a passband with geometric (log frequency) symmetry about wo.

Added in version 1.1.0.

Array API Standard Support

lp2bp_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

Use the ‘zpk’ (Zero-Pole-Gain) representation of a lowpass filter to transform it to a bandpass filter with a center frequency wo and bandwidth bw.

>>> from scipy.signal import lp2bp_zpk
>>> z   = [ 5 + 2j ,  5 - 2j ]
>>> p   = [ 7      ,  -16    ]
>>> k   = 0.8
>>> wo  = 0.62
>>> bw  = 15
>>> lp2bp_zpk(z, p, k, wo, bw)
(   array([7.49955815e+01+3.00017676e+01j, 7.49955815e+01-3.00017676e+01j,
           4.41850748e-03-1.76761126e-03j, 4.41850748e-03+1.76761126e-03j]),
    array([1.04996339e+02+0.j, -1.60167736e-03+0.j,  3.66108003e-03+0.j,
           -2.39998398e+02+0.j]), 0.8)