scipy.signal.

normalize#

scipy.signal.normalize(b, a)[source]#

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

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

Parameters:

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

Returns:

numarray: 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.
den1-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 support for Python Array API Standard compatible backends in addition to NumPy. 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

>>> 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
array([1.5, 3. ])
>>> den
array([ 1. , -2.5,  2. ])

>>> print(w[0].message)
Badly conditioned filter coefficients (numerator): the results may be meaningless