FiltWNoiseGenerator¶

class acoular.signals.FiltWNoiseGenerator¶

Bases: WNoiseGenerator

Generate filtered white noise using an AR, MA, or ARMA process.

• AR: autoregressive (ar)

• MA: moving-average (ma)

• ARMA: autoregressive moving-average

This class extends the WNoiseGenerator class to apply a digital filter to white noise, producing a signal with specific characteristics based on the provided filter coefficients. The desired filter is defined using the autoregressive coefficients (ar) and moving-average coefficients (ma).

The filter is implemented as a series of second-order sections (sos) for numerical stability, especially at high filter orders.

See also

WNoiseGenerator

For white noise generation.

Notes

• The output signal is adjusted for the group delay introduced by the filter, ensuring proper alignment of the filtered signal.

• The RMS value specified in the rms attribute corresponds to the original white noise signal and not the filtered output.

Examples

Generate filtered white noise using AR and MA coefficients:

>>> import acoular as ac
>>> import numpy as np
>>>
>>> # Define AR and MA coefficients
>>> ar = np.array([1.0, -0.5])
>>> ma = np.array([0.5, 0.5])
>>>
>>> # Create generator
>>> gen = ac.FiltWNoiseGenerator(
...     rms=1.0,
...     seed=42,
...     sample_freq=1000,
...     num_samples=10000,
...     ar=ar,
...     ma=ma,
... )
>>>
>>> # Generate signal
>>> signal = gen.signal()
>>> print(signal[:10])  # Print the first 10 samples
[0.24835708 0.30340346 0.40641385 1.28856612 1.2887213  0.41021549
 0.87764567 1.61214661 0.95505348 0.51406957]

ar = CArray(value=array([]), dtype=float, desc='autoregressive coefficients (coefficients of the denominator)')¶

A numpy.ndarray of autoregressive coefficients (denominator). Default is [], which results in no AR filtering (i.e., all-pole filter is [1.0]).

ma = CArray(value=array([]), dtype=float, desc='moving-average coefficients (coefficients of the numerator)')¶

A numpy.ndarray of moving-average coefficients (numerator). Default is [], which results in no MA filtering (i.e., all-zero filter is [1.0]).

digest = Property(depends_on=['rms', 'seed', 'sample_freq', 'num_samples', 'ar', 'ma'])¶

A unique checksum identifier based on the object properties. (read-only)

handle_empty_coefficients(coefficients)¶

Handle empty filter coefficient arrays by returning a default value.

This method ensures that both the autoregressive (ar) and moving-average (ma) coefficients are non-empty before filtering. If a coefficient array is empty, it is replaced with a default array containing a single value of 1.0.

Parameters:

coefficientsnumpy.ndarray

Array of filter coefficients to check.

Returns:

numpy.ndarray

The original array if it is non-empty, or a default array containing [1.0] if the input array is empty.

signal()¶

Generate and return the filtered white noise signal.

This method creates a white noise signal with the specified RMS value and seed, then filters it using the autoregressive (ar) and moving-average (ma) coefficients. The filtering process compensates for group delay introduced by the filter.

Returns:

numpy.ndarray of floats

An array representing the filtered white noise signal. The length of the returned array is equal to the number of samples.