Types§

Types provided by TLT.

Note

To create instances of these types, use the factory functions provided at the top level. For example, use time_series() to construct a TimeSeries object.

Warning

The __init__ methods of these classes are not part of the public API, and may change without deprecation.

Representations§

Representations are the most fundamental types in TLT, and are components of other more involved types.

They house numerical signal arrays, together with time and/or frequency grids and other metadata. They support not only basic algebraic operations as the underlying arrays do, but also some grid-aware operations such as semantic subsetting and embedding.

`TimeSeries`	A series of numbers on a time grid.
`UniformTimeSeries`	A time series on a uniform time grid.
`FrequencySeries`	A series of numbers on a frequency grid.
`UniformFrequencySeries`	A frequency series on a uniform frequency grid.
`TimePhasor`	Time-domain phasor representation.
`FrequencyPhasor`	Frequency-domain phasor representation.
`ShortTimeFourierTransform`	Short-time Fourier transform time-frequency representation.
`WilsonDaubechiesMeyer`	Wilson-Daubechies-Meyer time-frequency representation.
`STFT`	Alias for `ShortTimeFourierTransform`.
`WDM`	Alias for `WilsonDaubechiesMeyer`.

Data§

Data objects house multi-channel LISA data, where all channels are of the same representation type suitable for representing recorded data.

`TSData`	Multi-channel time series data container.
`FSData`	Multi-channel frequency series data container.
`TimedFSData`	Multi-channel frequency series data with time information.
`STFTData`	Multi-channel short-time Fourier transform data container.
`WDMData`	Multi-channel wavelet domain model data container.

Waveforms§

Similar to data objects, waveform objects group multiple representations together. Waveform objects are meant to represent modeled signals, and as such, they can carry theoretical information such as harmonic content, which is not the case for data objects.

In the nomenclature of the project, “raw” waveforms are detector-independent strains, such as the two polarizations (\(h_+\) and \(h_\times\)) or the spherical harmonic decomposition (\(h_{lm}\)); “projected” waveforms depend on LISA’s response, and are typically TDI channel signals.

`HarmonicWaveform`	Multi-mode waveform.
`HomogeneousHarmonicWaveform`	Multi-mode waveform where all modes share the same grid.
`PlusCrossWaveform`	Waveform in plus and cross polarizations.
`ProjectedWaveform`	Single-mode or mode-summed waveform projected onto the detector response in different channels.
`HarmonicProjectedWaveform`	Multi-mode waveform projected onto the detector response in different channels.
`HomogeneousHarmonicProjectedWaveform`	Multi-mode waveform where all modes share the same grid, projected onto the detector response in different channels.

Modes§

We use tuples of integers to label the modes of gravitational wave signals. Internally, these tuples are casted to Harmonic or QuasiNormalMode objects, which provide more semantic access to the components.

As the casting is done internally, users can just use normal tuples like (2, 2) to label the modes when constructing waveforms, or when accessing signal in some modes.

`Harmonic`	A harmonic mode.
`QuasiNormalMode`	A quasinormal mode.
`QNM`	Alias for `QuasiNormalMode`.

Spectral Density Matrices§

Matrices of Cross Spectral Densities (CSDs) and Power Spectral Densities (PSDs).

These are fundamental objects in the construction of noise models and likelihoods.

`SpectralDensity`	Represent the spectral density matrix (SDM) of a frequency domain stationary noise model.
`DiagonalSpectralDensity`	Represent a SDM for a frequency domain stationary noise model with no inter-channel correlations.
`EvolutionarySpectralDensity`	Evolutionary spectral density matrix (ESDM) for a time-frequency noise model.

Noise Models§

`FDNoiseModel`	Frequency domain noise model.
`TFNoiseModel`	Time-frequency Gaussian noise model.

Likelihoods§

FDWhittleLikelihood

Whittle likelihood for frequency-domain data.

Miscellaneous§

`Array`	An array from any array library supporting the Python Array API standard.
`ArrayFunc`	A callable that takes an `array` as input and returns an `array` as output.
`Interpolator`	A callable providing interpolation functionality.
`Grid1D`	A tuple containing a single axis, representing a 1D grid.
`Grid2DCartesian`	A tuple containing two axes, representing a dense 2D grid.
`Grid2DSparse`	Class for a sparse 2D grid.
`Grid2D`	A 2D grid, which is either `Grid2DCartesian` or `Grid2DSparse`.
`UniformGrid2D`	A tuple containing two `Linspace` axes, representing a uniform 2D grid.
`AnyGrid`	A grid that can be either 1D or 2D.
`Domain`	A type representing the physical domain of a representation, which can be either "time", "frequency", or "time-frequency".

`Axis`	An axis of a grid.
`Linspace`	A lazy representation of a uniformly spaced array.
`IntegrationMethod`	Name of the numerical integration method.
`IntegrationPolicy`	Protocol for quadrature policies used by noise models.