Stochastic Signals

lisatools.stochastic.get_stock_gb_stochastic_options() → List[StochasticContribution]

Get stock options for stochastic contributions.

Returns:

List of stock stochastic options.

lisatools.stochastic.get_default_stochastic_from_str(stochastic: str) → StochasticContribution

Return a LISA stochastic from a str input.

Parameters:

stochastic – Stochastic contribution indicated with a str.

Returns:

Stochastic contribution associated to that str.

lisatools.stochastic.check_stochastic(stochastic: Any) → StochasticContribution

Check input stochastic contribution.

Parameters:

stochastic – Stochastic contribution to check.

Returns:

Stochastic contribution checked. Adjusted from str if str input.

Stochastic Base Class

class lisatools.stochastic.StochasticContribution

Bases: ABC

Base Class for Stochastic Contributions to the PSD.

classmethod get_Sh(f: float | ndarray, *params: ndarray | list, **kwargs: Any) → float | ndarray

Calculate the power spectral density of the stochastic contribution.

Parameters:

  • f – Frequency array.

  • *params – Parameters for the stochastic model.

  • **kwargs – Keyword arguments for the stochastic model.

static specific_Sh_function(f: float | ndarray, *args: Any, **kwargs: Any) → float | ndarray

Calculate the power spectral density contained in a stochastic signal contribution.

Parameters:

  • f – Frequency array.

  • *args – Any arguments for the function.

  • **kwargs – Any keyword arguments for the function.

Returns:

Power spectral density contained in stochastic signal.

Combinatorial Stochastic Container

class lisatools.stochastic.StochasticContributionContainer(stochastic_contribution_dict: dict[StochasticContribution])

Bases: object

Container for multiple Stochastic Contributions

Parameters:

stochastic_contribution_dict – Dictionary with multiple Stochastic entries. Keys are the names and values are of type StochasticContribution.

property stochastic_contribution_dict: dict[StochasticContribution]

Stochastic contribution storage.

get_Sh(f: float | ndarray, params_dict: dict[tuple], kwargs_dict: dict[dict]) → ndarray

Calculate Sh for stochastic contribution.

Parameters:

  • f – Frequency array.

  • params_dict – Dictionary with keys equivalent to self.stochastic_contribution_dict.keys(). Values are the parameters for each associated model.

  • kwargs_dict – Dictionary with keys equivalent to self.stochastic_contribution_dict.keys(). Values are the keyword argument dicts for each associated model.

Returns:

Stochastic contribution.

Stock Stochastic Models

class lisatools.stochastic.HyperbolicTangentGalacticForeground

Bases: StochasticContribution

Hyperbolic Tangent-based foreground fitting function.

static specific_Sh_function(f: float | ndarray, amp: float, fk: float, alpha: float, s1: float, s2: float) → float | ndarray

Hyperbolic tangent model 1 for the Galaxy foreground noise

This model for the PSD contribution from the Galactic foreground noise is given by

\[S_\text{gal} = \frac{A_\text{gal}}{2}e^{-s_1f^\alpha}f^{-7/3}\left[ 1 + \tanh{\left(-s_2 (f - f_k)\right)} \right],\]

where \(A_\text{gal}\) is the amplitude of the stochastic signal, \(f_k\) is the knee frequency at which a bend occurs, math:alpha is a power law parameter, \(s_1\) is a slope parameter below the knee, and \(s_2\) is a slope parameter after the knee.:

Parameters:

  • f – Frequency array.

  • amp – Amplitude parameter for the Galaxy.

  • fk – Knee frequency in Hz.

  • alpha – Power law parameter.

  • s1 – Slope parameter below knee.

  • s2 – Slope parameter above knee.

Returns:

PSD of the Galaxy foreground noise

class lisatools.stochastic.FittedHyperbolicTangentGalacticForeground

Bases: HyperbolicTangentGalacticForeground

classmethod specific_Sh_function(f: float | ndarray, Tobs: float) → float | ndarray

Fitted hyperbolic tangent model 1 for the Galaxy foreground noise.

This class fits the parameters for HyperbolicTangentGalacticForeground using analytic estimates from (# TODO). The fit is a function of time, so the user inputs Tobs.

# Sgal_1d = 2.2e-44*np.exp(-(fr**1.2)*0.9e3)*(fr**(-7./3.))*0.5*(1.0 + np.tanh(-(fr-1.4e-2)*0.7e2)) # Sgal_3m = 2.2e-44*np.exp(-(fr**1.2)*1.7e3)*(fr**(-7./3.))*0.5*(1.0 + np.tanh(-(fr-4.8e-3)*5.4e2)) # Sgal_1y = 2.2e-44*np.exp(-(fr**1.2)*2.2e3)*(fr**(-7./3.))*0.5*(1.0 + np.tanh(-(fr-3.1e-3)*1.3e3)) # Sgal_2y = 2.2e-44*np.exp(-(fr**1.2)*2.2e3)*(fr**(-7./3.))*0.5*(1.0 + np.tanh(-(fr-2.3e-3)*1.8e3)) # Sgal_4y = 2.2e-44*np.exp(-(fr**1.2)*2.9e3)*(fr**(-7./3.))*0.5*(1.0 + np.tanh(-(fr-2.0e-3)*1.9e3))

Parameters:

  • f – Frequency array.

  • Tobs – Observation time in seconds.

Returns:

PSD of the Galaxy foreground noise