Frequency-domain fitting

Frequency-domain fitting extends the same single-fit, global-fit, and parameter-trending workflow used in the time domain to displayed Fourier spectra. The V1 workflow fits the real-valued spectrum currently shown in the Frequency view. It does not fit the complex FFT directly.

The spectrum you fit can come from either quantitative estimator — the FFT or maximum entropy; pick one with Choosing a spectral estimator: FFT, MaxEnt, or Burg. (The Burg Resolution view is a line-count diagnostic, not a fit target.) Computing and conditioning that spectrum in the first place is covered by Fourier analysis.

Workflow

Compute a Fourier spectrum from the Fourier panel.
Switch to the Frequency workspace.
Open the Fit dock.
Fit the displayed spectrum with a Gaussian or Lorentzian peak plus a constant or linear background.
For a run series, select multiple runs with cached spectra and use the Global tab.
Inspect nu0 and fwhm in the Parameters dock, alongside derived B0 and Bwid field equivalents.

The fitting x axis is stored internally as absolute frequency in MHz. Plotting controls may show field in gauss or a reference-relative frequency axis, but fit parameters remain canonical: nu0 and fwhm are MHz quantities.

Fit range and seeding

The fit range (≤ ν ≤, in MHz) restricts the fit to a band of the spectrum. As in the time domain, the band is drawn on the plot as a shaded span with dashed edges, and either edge can be dragged directly on the spectrum or typed into the range fields. When the frequency axis is displayed in gauss or relative to a reference field the span follows the displayed units, but the range is always entered and stored as absolute MHz.

Peak parameters are seeded automatically from the displayed spectrum: the centre nu0, height, and width are read from the dominant peak of the run being fitted, so Preview draws the peak in place before you fit. Because the peak position tracks each run’s applied field, these seeds are re-derived for every run rather than carried across a run series.

When the model carries more than one peak (add a second GaussianPeak or LorentzianPeak from the fit-function builder), each peak component is seeded from a distinct line in the spectrum — the strongest detected peak seeds the first component, the next strongest the second, and so on. Adding a peak component is read as “a line exists here”, so a weak-but-real shoulder is seeded rather than gated out. If the spectrum shows fewer lines than the model declares, the surplus components are spread across the fit window so they stay visible in the preview instead of collapsing to an off-screen default.

Available components

The fit-function builder is filtered by analysis domain: when fitting a spectrum it offers only the frequency-domain components below (as a flat list), and these components do not appear when fitting in the time domain. Typing a component name from the other domain gives an explanatory error.

GaussianPeak: Peak height, centre nu0, and full width at half maximum fwhm.
LorentzianPeak: Peak height, centre nu0, and full width at half maximum fwhm.
ConstantBackground: Flat spectral background bg.
LinearBackground: Background bg + slope * nu.

Global fits and trends

Global frequency-domain fitting uses the same parameter-role table as time-domain global fitting. Mark peak centre or width as Local to trend them across a field or temperature series, or mark background terms as Global when they should be shared.

Successful global frequency fits are sent to the Parameters dock under the Frequency Domain group. The parameter-trending tools can then fit nu0(T), fwhm(B), B0(T), or Bwid(B) using the usual trend-model workflow.

Project files

Project files store frequency-fit state separately from time-domain fit state. This lets a project reopen with both a time-domain model and a spectral peak model intact. Cached Fourier spectra are still stored in the Fourier spectrum state; raw detector arrays remain referenced by source-file path rather than embedded in the project.

Note

The Gaussian and Lorentzian peak forms fitted here are the ordinary line shapes; the minimiser and its statistics are the shared engine documented in Fitting engine. Because the fit target is the displayed real spectrum, an apodised or baseline-subtracted spectrum carries those conditioning choices into the fitted width and amplitude — see the apodisation caveat in Fourier analysis and the conditioning steps in Frequency-domain conditioning. This page therefore adds no new physics of its own; the underlying references are those of Fitting engine and Fourier analysis.