PowerSpectra¶

class acoular.spectra.PowerSpectra¶

Bases: BaseSpectra

Provides the cross-spectral matrix of multichannel time-domain data and its eigen-decomposition.

This class is designed to compute the cross-spectral matrix (CSM) efficiently using the Welch method [19] with support for windowing and overlapping data segments. It also calculates the eigenvalues and eigenvectors of the CSM, allowing for spectral analysis and advanced signal processing tasks.

Key features:

• Efficient Calculation: Computes the CSM using FFT-based methods.

• Caching: Results can be cached in HDF5 files to avoid redundant calculations for identical inputs and parameters.

• Lazy Evaluation: Calculations are triggered only when attributes like csm, eva, or eve are accessed.

• Dynamic Input Handling: Automatically recomputes results when the input data or parameters change.

source = Instance(SamplesGenerator)¶

The data source for the time-domain samples. It must be an instance of SamplesGenerator or a derived class.

ind_low = Property(_ind_low, desc='index of lowest frequency line')¶

Index of lowest frequency line to compute. Default is 1. Only used by objects that fetch the CSM. PowerSpectra computes every frequency line.

ind_high = Property(_ind_high, desc='index of lowest frequency line')¶

Index of highest frequency line to compute. Default is -1 (last possible line for default block_size).

cached = Bool(True, desc='cached flag')¶

A flag indicating whether the result should be cached in HDF5 files. Default is True.

num_blocks = Property(desc='overall number of FFT blocks')¶

The number of FFT blocks used for averaging. This is derived from the block_size and overlap parameters. (read-only)

freq_range = Property(desc='frequency range')¶

2-element array with the lowest and highest frequency. If the higher frequency is larger than the max frequency, the max frequency will be the upper bound.

indices = Property(desc='index range')¶

The sequence of frequency indices between ind_low and ind_high. (read-only)

basename = Property(depends_on=['source.digest'], desc='basename for cache file')¶

The name of the cache file (without the file extension) used for storing results. (read-only)

csm = Property(desc='cross spectral matrix')¶

The cross-spectral matrix, represented as an array of shape (n, m, m) of complex values for n frequencies and m channels as in num_channels. (read-only)

eva = Property(desc='eigenvalues of cross spectral matrix')¶

The eigenvalues of the CSM, stored as an array of shape (n,) of floats for n frequencies. (read-only)

eve = Property(desc='eigenvectors of cross spectral matrix')¶

The eigenvectors of the cross spectral matrix, stored as an array of shape (n, m, m) of floats for n frequencies and m channels as in num_channels. (read-only)

digest = Property( …¶

A unique identifier for the spectra, based on its properties. (read-only)

h5f = Instance(H5CacheFileBase, transient=True)¶

The HDF5 cache file used for storing the results if cached is set to True.

calc_csm()¶

Calculate the CSM for the given source data.

This method computes the CSM by performing a block-wise Fast Fourier Transform (FFT) on the source data, applying a window function, and averaging the results. Only the upper triangular part of the matrix is computed for efficiency, and the lower triangular part is constructed via transposition and complex conjugation.

Returns:

numpy.ndarray

The computed cross spectral matrix as an array of shape (n, m, m) of complex values for n frequencies and m channels as in num_channels.

Examples

>>> import numpy as np
>>> from acoular import TimeSamples
>>> from acoular.spectra import PowerSpectra
>>>
>>> data = np.random.rand(1000, 4)
>>> ts = TimeSamples(data=data, sample_freq=51200)
>>> print(ts.num_channels, ts.num_samples, ts.sample_freq)
4 1000 51200.0
>>> ps = PowerSpectra(source=ts, block_size=128, window='Blackman')
>>> ps.csm.shape
(65, 4, 4)

calc_ev()¶

Calculate eigenvalues and eigenvectors of the CSM for each frequency.

The eigenvalues represent the spectral power, and the eigenvectors correspond to the principal components of the matrix. This calculation is performed for all frequency slices of the CSM.

Returns:

tuple of numpy.ndarray

A tuple containing:

• eva (numpy.ndarray): Eigenvalues as a 2D array of shape (n, m), where n is the number of frequencies and m is the number of channels. The datatype depends on the precision.

• eve (numpy.ndarray): Eigenvectors as a 3D array of shape (n, m, m). The datatype is consistent with the precision of the input data.

Notes

• The precision of the eigenvalues is determined by precision ('float64' for complex128 precision and 'float32' for complex64 precision).

• This method assumes the CSM is already computed and accessible via csm.

Examples

>>> import numpy as np
>>> from acoular import TimeSamples
>>> from acoular.spectra import PowerSpectra
>>>
>>> data = np.random.rand(1000, 4)
>>> ts = TimeSamples(data=data, sample_freq=51200)
>>> ps = PowerSpectra(source=ts, block_size=128, window='Hanning')
>>> eva, eve = ps.calc_ev()
>>> print(eva.shape, eve.shape)
(65, 4) (65, 4, 4)

calc_eva()¶

Calculate eigenvalues of the CSM.

This method computes and returns the eigenvalues of the CSM for all frequency slices.

Returns:

numpy.ndarray

A 2D array of shape (n, m) containing the eigenvalues for n frequencies and m channels. The datatype depends on precision ('float64' for complex128 precision and 'float32' for complex64 precision).

Notes

This method internally calls calc_ev() and extracts only the eigenvalues.

calc_eve()¶

Calculate eigenvectors of the Cross Spectral Matrix (CSM).

This method computes and returns the eigenvectors of the CSM for all frequency slices.

Returns:

numpy.ndarray

A 3D array of shape (n, m, m) containing the eigenvectors for n frequencies and m channels. Each slice eve[f] represents an (m, m) matrix of eigenvectors for frequency f. The datatype matches the precision of the CSM (complex128 or complex64).

Notes

This method internally calls calc_ev() and extracts only the eigenvectors.

synthetic_ev(freq, num=0)¶

Retrieve synthetic eigenvalues for a specified frequency or frequency range.

This method calculates the eigenvalues of the CSM for a single frequency or a synthetic frequency range. If num is set to 0, it retrieves the eigenvalues at the exact frequency. Otherwise, it averages eigenvalues across a range determined by freq and num.

Parameters:

freqfloat

The target frequency for which the eigenvalues are calculated. This is the center frequency for synthetic averaging.

numint, optional

The number of subdivisions in the logarithmic frequency space around the center frequency freq.

• 0 (default): Only the eigenvalues for the exact frequency line are returned.

• Non-zero:

num	frequency band width
0	single frequency line
1	octave band
3	third-octave band
n	1/n-octave band

Returns:

numpy.ndarray

An array of eigenvalues. If num == 0, the eigenvalues for the single frequency are returned. For num > 0, a summed array of eigenvalues across the synthetic frequency range is returned.

Examples

>>> import numpy as np
>>> from acoular import TimeSamples
>>> from acoular.spectra import PowerSpectra
>>> np.random.seed(0)
>>>
>>> data = np.random.rand(1000, 4)
>>> ts = TimeSamples(data=data, sample_freq=51200)
>>> ps = PowerSpectra(source=ts, block_size=128, window='Hamming')
>>> ps.synthetic_ev(freq=5000, num=5)
array([0.00048803, 0.0010141 , 0.00234248, 0.00457097])
>>> ps.synthetic_ev(freq=5000)
array([0.00022468, 0.0004589 , 0.00088059, 0.00245989])