SpectralDensity

class typed_lisa_toolkit.types.SpectralDensity

Represent the spectral density matrix (SDM) of a frequency domain stationary noise model.

Note

The SDM is a real-valued, symmetric, positive-definite matrix, hence it is invertible. It is the inverse SDM that is used in the inner product and whitening operations, and we store the inverse SDM in this representation.

Note

To construct a SpectralDensity, use the make_sdm() factory function.

get_kernel(backend: str | None = None) → Array[Any, ModuleType] | ndarray[tuple[Any, ...], dtype[Any]]

Return the inverse of the spectral density matrix.

The inverse SDM is returned as an array of shape (n_freqs, n_channels, n_channels).

Note

We denote the inverse SDM as \(S_n^{-1}\).

get_whitening_matrix(kind: Literal['cholesky'] | None = 'cholesky') → Array[Any, ModuleType] | ndarray[tuple[Any, ...], dtype[Any]]

Return whitening matrix \(W\) with shape (n_freqs, n_channels, n_channels).

The whitening matrix represents a linear transformation that yields unit variance white noise when applied to noise that follows this model. This is useful in detecting deviations from the model.

Note

\(W\) satisfies \(S_n^{-1} = W^\top W\).

to_subband(f_interval: tuple[float, float]) → Self

Return a new SpectralDensity instance with the frequency grid restricted to the given subband.