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

ma: 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: 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.

usignal(factor)

Resample the signal at a higher sampling frequency.

This method uses Fourier transform-based resampling to deliver the signal at a sampling frequency that is a multiple of the original sample_freq. The resampled signal has a length of factor * num_samples.

Parameters:

factorint: The resampling factor. Defines how many times larger the new sampling frequency is compared to the original sample_freq.

Returns:

numpy.ndarray: The resampled signal as a 1D array of floats.

Notes

This method relies on the scipy.signal.resample() function for resampling.

Examples

Resample a signal by a factor of 4:

>>> from acoular import SineGenerator  # Class extending SignalGenerator
>>> sg = SineGenerator(sample_freq=100.0, num_samples=1000)
>>> resampled_signal = sg.usignal(4)
>>> len(resampled_signal)
4000

rms: Root mean square (RMS) amplitude of the signal. For a point source, this corresponds to the RMS amplitude at a distance of 1 meter. Default is 1.0.

seed: Seed for random number generator. Default is 0. This parameter should be set differently for different instances to guarantee statistically independent (non-correlated) outputs.

sample_freq: Sampling frequency of the signal in Hz. Default is 1.0.

num_samples: The number of samples to generate for the signal.

FiltWNoiseGenerator#

`FiltWNoiseGenerator`#