spectrochempy.PSD

class PSD(*, log_level='WARNING', demodulation='matrix', harmonic=1, integration_rule='trapezoid', n_spectra_per_cycle=None, phase_unit='degrees', phi)[source]

PSD (Phase-Sensitive Detection) for demodulating spectroscopic data.

PSD is a deterministic signal-processing transform, analogous to FFT or Hilbert transforms. It does not learn from data and stores no model state.

Supports two demodulation strategies:

Matrix transform demodulation: A_demodulated = T · A_averaged
Explicit integration demodulation: A_demodulated(φ, λ) = (2/period) ∫ A_averaged(t, λ) · sin(k·ω·t + φ) dt

Parameters

demodulation ({“matrix”, “integration”}, default=”matrix”) – Demodulation strategy. Matrix demodulation is the default because it is generally faster for trapezoid and Simpson rules, while producing results equivalent to explicit integration.
harmonic (int, default=1) – Demodulation harmonic index (k in sin(k*ω*t + phi)).
integration_rule ({“riemann”, “trapezoid”, “simpson”}, default=”trapezoid”) – Integration rule for numerical integration weights. "riemann" uses a right-endpoint rectangular rule over n equal subintervals of [0, 1], sampling at t = (i+1)/n. This rule gives exact results for pure sinusoids at any n.
n_spectra_per_cycle (int or None, default=None) – Number of spectra per cycle. If None, inferred from data shape.
phase_unit ({“degrees”, “radians”}, default=”degrees”) – Unit for phase output.
phi (array-like, default=np.arange(0.0, 360.0, 15.0)) – Phase angles for demodulation (in degrees).

Notes

Requires phi to contain 0° and 90° for in_phase/quadrature extraction.
Matrix demodulation is default and faster.
Integration demodulation uses explicit numerical integration with a configurable integration rule.
The "riemann" rule uses a right-endpoint rectangular grid t = (i+1)/n independent of the actual time coordinate; for irregular time coordinates use "trapezoid" or "simpson".
Constant offsets (DC) do not affect the PSD result because sinusoidal demodulation functions integrate to zero over one complete modulation period. No explicit mean subtraction is necessary.

Math notation:

T = transform matrix (shape: n_phi × n_spectra_per_cycle)
period = modulation period (from time coordinate)
ω = 2π / period (angular frequency)
harmonic = k (demodulation harmonic index)

PSD equation (matrix method):

A_demodulated = T · A_averaged

where A_averaged has shape (n_spectra_per_cycle, n_channels), averaged across all cycles.

PSD equation (integration method):

A_demodulated (φ, λ) = (2/period) ∫ A_averaged(t, λ) · sin(k·ω·t_rel + φ) dt

where φ is the demodulation phase angle, λ is the channel, and t_rel is normalized relative time within one modulation period (t_rel = 0 at the start of the period, t_rel = 1 at the end).

Examples

>>> import spectrochempy as scp
>>> # Raw 2D input (120 spectra, 1000 channels)
>>> X = scp.random(size=(120, 1000))
>>> psd = scp.PSD(n_spectra_per_cycle=60, demodulation='matrix')
>>> result = psd.transform(X)
>>> result.in_phase
>>> result.quadrature
>>> result.amplitude
>>> result.phase

Initialize the BaseConfigurable class.

Parameters

log_level (int, optional) – The log level at startup. Default is logging.WARNING.
**kwargs (dict) – Additional keyword arguments for configuration.

Attributes Summary

`config`	`traitlets.config.Config` object.
`demodulation`	An enum whose value must be in a given sequence.
`harmonic`	Demodulation harmonic index.
`integration_rule`	An enum whose value must be in a given sequence.
`log`	Return `log` output.
`n_spectra_per_cycle`	Number of spectra per cycle.
`name`	Object name
`phase_unit`	An enum whose value must be in a given sequence.
`phi`	Phase angles for demodulation (in degrees).

Methods Summary

`inverse_transform`([X_transform])	Inverse transform is not supported for PSD.
`params`([default])	Return current or default configuration values.
`reset`()	Reset configuration parameters to their default values.
`to_dict`()	Return config value in a dict form.
`transform`(X)	Apply the PSD transform to data X.

Attributes Documentation

config: traitlets.config.Config object.

demodulation: An enum whose value must be in a given sequence.

harmonic: Demodulation harmonic index.

integration_rule: An enum whose value must be in a given sequence.

log: Return log output.

n_spectra_per_cycle: Number of spectra per cycle.

name: Object name

phase_unit: An enum whose value must be in a given sequence.

phi: Phase angles for demodulation (in degrees).

Methods Documentation

inverse_transform(X_transform=None, **kwargs)[source]

Inverse transform is not supported for PSD.

Raises: NotImplementedError – Always raised as PRS is not invertible.

params(default=False)[source]

Return current or default configuration values.

Parameters: default (bool, optional, default: False) – If default is True, the default parameters are returned, else the current values.
Returns: dict – Current or default configuration values.

reset()[source]: Reset configuration parameters to their default values.

to_dict()[source]

Return config value in a dict form.

Returns: dict – A regular dictionary.

transform(X)[source]

Apply the PSD transform to data X.

All inputs are internally normalized into a single cycle-averaged 2D modulation waveform A(t, ν) before demodulation.

This is a pure computation that does not mutate internal state. Repeated calls are independent and thread-safe.

Parameters: X (NDDataset or array-like) – Input data for PSD.
Returns: PSDResult – Container with prs, in_phase, quadrature, amplitude, phase, and T.

Examples using spectrochempy.PSD