bcam.indar.ema.SuperResolution

class bcam.indar.ema.SuperResolution(*, order: int = 2, rational_fitter={'method': 'AAA'}, damping: float = 0.0, fs: float = 1.0, prune_tol: float = 0.0, compute_amps: bool = True)

Spectral estimation based on rational fitting.

This class approximate a signal with an exponential sum. If

\[f_k = \sum_{j=0}^{M-1} a_j e^{\lambda_j k\,dt},\quad k = 0, \ldots, n-1,\]

where \(a_j\) are the amplitudes, and \(\lambda_j\) are complex exponents, then the DFT is

\[e^{-2\pi i k/n}\hat{f}_k = \sum_{j=0}^{M-1} \frac{a_j(1-e^{\lambda_j n\,dt})}{e^{2\pi i k/n}-e^{\lambda_j\,dt}},\quad k = 0, \ldots, n-1,\]

which enables the use of rational approximation. The algorithm follows a similar pattern as in ESPIRA.

Parameters:

orderint, default 2

Number of poles used by the internal rational fitter.

rational_fitterdict, default {‘method’: ‘AAA’}

Configuration dictionary for the rational fitter. It must include the key method with value 'AAA' or 'VF'. Any additional keys are forwarded to the selected estimator constructor.

dampingfloat, default 0.

Exponential damping factor applied to the time signal before fitting. Set to 0. to disable damping.

fsfloat, default 1.

Sampling frequency (\(= 1/dt\)) used to scale continuous-time exponents.

prune_tolfloat, default 0.

Tolerance for pruning poles based on the norm of the fitted amplitudes.

compute_ampsbool, default True

Whether to compute and store amplitudes after fitting poles.

Attributes:

poles_Poles

Estimated stable poles after optional pruning.

amps_HCoeffs or None

Estimated amplitudes if compute_amps=True; otherwise None.

exps_HCoeffs

Continuous-time exponents computed as log(poles_) * fs.

n_poles_int

Number of poles identified by the internal rational fitter.

Methods

fit(y)	Fit exponential sum.
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict using the exponential sum.
set_params(**params)	Set the parameters of this estimator.

fit(y: array - like) → SuperResolution

Fit exponential sum.

Parameters:

yarray-like, shape (n_samples, n_channels)

Time-domain signal to fit, where \(y_k\) is a vector of length n_channels for each time index \(k = 0, \ldots, n-1\).

Returns:

selfSuperResolution

Fitted estimator.

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

predict(X: array - like) → ndarray

Predict using the exponential sum.

Parameters:

Xarray-like, shape (n_eval_points,)

Time points at which to evaluate the exponential sum.

Returns:

fnp.ndarray, shape (n_eval_points, n_channels)

Predicted values. If compute_amps=False, then the returned values are NaN.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.