scipy.signal.

lp2lp_zpk#

scipy.signal.lp2lp_zpk(z, p, k, wo=1.0)[source]#

Transform a lowpass filter prototype to a different frequency.

Return an analog low-pass filter with cutoff frequency wo 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 cutoff, as angular frequency (e.g., rad/s). Defaults to no change.

Returns:

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

See also

lp2hp_zpk, lp2bp_zpk, lp2bs_zpk, bilinear
lp2lp

Notes

This is derived from the s-plane substitution

\[s \rightarrow \frac{s}{\omega_0}\]

Added in version 1.1.0.

Array API Standard Support

lp2lp_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 new ‘zpk’ representation associated with a cutoff frequency wo.

>>> from scipy.signal import lp2lp_zpk
>>> z   = [7,   2]
>>> p   = [5,   13]
>>> k   = 0.8
>>> wo  = 0.4
>>> lp2lp_zpk(z, p, k, wo)
(   array([2.8, 0.8]), array([2. , 5.2]), 0.8)