`scipy.signal._filter_design:normalize`

source: /scipy/signal/_filter_design.py:1847

Signature

def normalize(b, a)

Summary

Normalize numerator/denominator of a continuous-time transfer function.

Extended Summary

If values of b are too close to 0, they are removed. In that case, a BadCoefficients warning is emitted.

Parameters

b : array_like: Numerator of the transfer function. Can be a 2-D array to normalize multiple transfer functions.
a : array_like: Denominator of the transfer function. At most 1-D.

Returns

num : array: The numerator of the normalized transfer function. At least a 1-D array. A 2-D array if the input num is a 2-D array.
den : 1-D array: The denominator of the normalized transfer function.

Notes

Coefficients for both the numerator and denominator should be specified in descending exponent order (e.g., s^2 + 3s + 5 would be represented as [1, 3, 5]).

Array API Standard Support

normalize 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

from scipy.signal import normalize

✓

Normalize the coefficients of the transfer function ``(3*s^2 - 2*s + 5) / (2*s^2 + 3*s + 1)``:

b = [3, -2, 5]
a = [2, 3, 1]
normalize(b, a)

✓

(array([ 1.5, -1. ,  2.5]), array([1. , 1.5, 0.5]))

A warning is generated if, for example, the first coefficient of `b` is 0. In the following example, the result is as expected:

import warnings
with warnings.catch_warnings(record=True, action='always') as w:
    num, den = normalize([0, 3, 6], [2, -5, 4])

✓

num
den

✓

array([ 1. , -2.5,  2. ])

print(w[0].message)

✓

Badly conditioned filter coefficients (numerator): the results may be meaningless

Aliases

scipy.signal.normalize