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Multi-Sensor

Tools for analysing relationships between multiple measurement channels: correlation matrices, coherence matrices, and the cross-spectral density matrix (input to FDD).

Multi-sensor example

dspkit.multisensor.correlation_matrix(data)

Pairwise Pearson correlation matrix for multi-channel data.

Parameters:

Name Type Description Default
data (array_like, shape(n_channels, N))

Each row is a time series from one sensor.

 required

Returns:

Name Type Description
R (ndarray, shape(n_channels, n_channels))

Correlation matrix with values in [-1, 1]. R[i, j] is the Pearson correlation coefficient between channels i and j.
Source code in dspkit/multisensor.py 
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def correlation_matrix(
    data: np.ndarray,
) -> np.ndarray:
    """
    Pairwise Pearson correlation matrix for multi-channel data.

    Parameters
    ----------
    data : array_like, shape (n_channels, N)
        Each row is a time series from one sensor.

    Returns
    -------
    R : ndarray, shape (n_channels, n_channels)
        Correlation matrix with values in [-1, 1].
        ``R[i, j]`` is the Pearson correlation coefficient between
        channels ``i`` and ``j``.
    """
    data = np.atleast_2d(np.asarray(data, dtype=float))
    return np.corrcoef(data)

dspkit.multisensor.coherence_matrix(data, fs, window='hann', nperseg=None, noverlap=None, detrend='constant')

Pairwise magnitude-squared coherence matrix.

Parameters:

Name Type Description Default
data (array_like, shape(n_channels, N))

Each row is a time series from one sensor.

 required
fs float

Sampling frequency [Hz].

 required
window str

Window function (default 'hann').

 'hann'
nperseg int or None

Welch segment length. Defaults to min(N, 1024).

 None
noverlap int or None

Overlap between segments.

 None
detrend str or False

Per-segment detrending.

 'constant'

Returns:

Name Type Description
freqs (ndarray, shape(M))

Frequency vector [Hz].
C (ndarray, shape(n_channels, n_channels, M))

Coherence matrix. C[i, j, :] is the magnitude-squared coherence between channels i and j. Diagonal entries are 1.0.
Source code in dspkit/multisensor.py 
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def coherence_matrix(
    data: np.ndarray,
    fs: float,
    window: str = "hann",
    nperseg: int | None = None,
    noverlap: int | None = None,
    detrend: str | Literal[False] = "constant",
) -> tuple[np.ndarray, np.ndarray]:
    """
    Pairwise magnitude-squared coherence matrix.

    Parameters
    ----------
    data : array_like, shape (n_channels, N)
        Each row is a time series from one sensor.
    fs : float
        Sampling frequency [Hz].
    window : str
        Window function (default ``'hann'``).
    nperseg : int or None
        Welch segment length. Defaults to ``min(N, 1024)``.
    noverlap : int or None
        Overlap between segments.
    detrend : str or False
        Per-segment detrending.

    Returns
    -------
    freqs : ndarray, shape (M,)
        Frequency vector [Hz].
    C : ndarray, shape (n_channels, n_channels, M)
        Coherence matrix. ``C[i, j, :]`` is the magnitude-squared coherence
        between channels ``i`` and ``j``. Diagonal entries are 1.0.
    """
    data = np.atleast_2d(np.asarray(data, dtype=float))
    n_ch, N = data.shape

    if nperseg is None:
        nperseg = min(N, 1024)

    # Compute one coherence to get the frequency vector length
    freqs, _ = _signal.coherence(
        data[0], data[0], fs=fs, window=window,
        nperseg=nperseg, noverlap=noverlap, detrend=detrend,
    )
    M = len(freqs)
    C = np.ones((n_ch, n_ch, M), dtype=float)

    for i in range(n_ch):
        for j in range(i + 1, n_ch):
            _, Cij = _signal.coherence(
                data[i], data[j], fs=fs, window=window,
                nperseg=nperseg, noverlap=noverlap, detrend=detrend,
            )
            C[i, j, :] = Cij
            C[j, i, :] = Cij

    return freqs, C

dspkit.multisensor.psd_matrix(data, fs, window='hann', nperseg=None, noverlap=None, detrend='constant')

Cross-spectral density matrix (power spectral density matrix).

Computes the full n_channels × n_channels CSD matrix at each frequency. This is the input required for Frequency Domain Decomposition (FDD).

The matrix is Hermitian at each frequency: G[i,j,f] = conj(G[j,i,f]). Diagonal entries G[i,i,f] are real-valued (auto-PSD).

Parameters:

Name Type Description Default
data (array_like, shape(n_channels, N))

Each row is a time series from one sensor.

 required
fs float

Sampling frequency [Hz].

 required
window str

Window function (default 'hann').

 'hann'
nperseg int or None

Welch segment length. Defaults to min(N, 1024).

 None
noverlap int or None

Overlap between segments.

 None
detrend str or False

Per-segment detrending.

 'constant'

Returns:

Name Type Description
freqs (ndarray, shape(M))

Frequency vector [Hz].
G (ndarray, shape(n_channels, n_channels, M), complex)

Cross-spectral density matrix. G[i, j, k] is the CSD between channels i and j at frequency freqs[k].
Source code in dspkit/multisensor.py 
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def psd_matrix(
    data: np.ndarray,
    fs: float,
    window: str = "hann",
    nperseg: int | None = None,
    noverlap: int | None = None,
    detrend: str | Literal[False] = "constant",
) -> tuple[np.ndarray, np.ndarray]:
    """
    Cross-spectral density matrix (power spectral density matrix).

    Computes the full n_channels × n_channels CSD matrix at each frequency.
    This is the input required for Frequency Domain Decomposition (FDD).

    The matrix is Hermitian at each frequency: ``G[i,j,f] = conj(G[j,i,f])``.
    Diagonal entries ``G[i,i,f]`` are real-valued (auto-PSD).

    Parameters
    ----------
    data : array_like, shape (n_channels, N)
        Each row is a time series from one sensor.
    fs : float
        Sampling frequency [Hz].
    window : str
        Window function (default ``'hann'``).
    nperseg : int or None
        Welch segment length. Defaults to ``min(N, 1024)``.
    noverlap : int or None
        Overlap between segments.
    detrend : str or False
        Per-segment detrending.

    Returns
    -------
    freqs : ndarray, shape (M,)
        Frequency vector [Hz].
    G : ndarray, shape (n_channels, n_channels, M), complex
        Cross-spectral density matrix. ``G[i, j, k]`` is the CSD between
        channels ``i`` and ``j`` at frequency ``freqs[k]``.
    """
    data = np.atleast_2d(np.asarray(data, dtype=float))
    n_ch, N = data.shape

    if nperseg is None:
        nperseg = min(N, 1024)

    # Get frequency vector length
    freqs, _ = _signal.csd(
        data[0], data[0], fs=fs, window=window,
        nperseg=nperseg, noverlap=noverlap, detrend=detrend,
    )
    M = len(freqs)
    G = np.zeros((n_ch, n_ch, M), dtype=complex)

    for i in range(n_ch):
        for j in range(i, n_ch):
            _, Gij = _signal.csd(
                data[i], data[j], fs=fs, window=window,
                nperseg=nperseg, noverlap=noverlap, detrend=detrend,
            )
            G[i, j, :] = Gij
            if i != j:
                G[j, i, :] = np.conj(Gij)

    return freqs, G