Describe › Signal & numerical

Peak deconvolution (fit overlapping peaks)

Multi-peak deconvolution fits a sum of overlapping lineshapes — Gaussian, Lorentzian or pseudo-Voigt — plus an optional baseline, reporting each component's centre, height, width and area.

What is Peak deconvolution (fit overlapping peaks)?

When peaks overlap, a single spectrum or chromatogram is the sum of several component bands. Deconvolution fits all components at once by nonlinear least squares, so each peak's parameters are estimated jointly rather than by cutting the signal into pieces. Each component is a textbook lineshape: a Gaussian (instrumental / Doppler broadening), a Lorentzian (lifetime broadening, slowly-decaying tails), or a pseudo-Voigt — the standard η·Lorentzian + (1−η)·Gaussian mixture that shares a single width and captures intermediate shapes.

Starting values come from derivative-sign peak detection (local maxima ranked by prominence, widths from the half-maximum span); the joint fit then refines every center, height and width together, with an optional constant or linear baseline. Peak area is the closed-form integral of each lineshape, so relative areas (percent of total) are exact given the fitted parameters.

With the number of peaks set to Auto, the model is fitted for k = 1…6 components and the k with the lowest AICc is reported — penalising extra peaks that don't earn their parameters.

When should I use Peak deconvolution (fit overlapping peaks)?

  • Resolving overlapping bands in spectroscopy (IR / Raman / UV-Vis / XPS) or chromatography.
  • Quantifying the relative area of each component when peaks are not baseline-resolved.
  • Estimating peak centers and widths that a simple maximum-finder can't separate.

What data does it need?

A signal column (+ optional X column for real units), the peak shape, the baseline model, and the number of peaks (or Auto).

What does it report?

An overlay chart of the raw signal, the total fit and each fitted component, plus a per-peak table (center, height, FWHM, area, % area with standard errors) and fit statistics (R², RMSE).

What does it assume?

  • Peaks are additive and follow the chosen lineshape; pick pseudo-Voigt when the shape is between Gaussian and Lorentzian.
  • Good initial peak detection matters — smooth very noisy data first (see smoothing).
  • The baseline is either flat, constant, or a straight line; strongly curved baselines should be corrected beforehand.

How do I interpret the result?

Compare the component overlay to the raw signal — systematic residual structure means too few peaks or the wrong lineshape.

Prefer percent-area over height for quantitation when widths differ between peaks.

Under Auto, a large AICc drop from k−1 to k signals a real extra component; a marginal drop does not.

See also

References

  • Wertheim, Butler, West & Buchanan (1974). Determination of the Gaussian and Lorentzian content of experimental line shapes.
  • Thompson, Cox & Hastings (1987). Rietveld refinement of Debye–Scherrer synchrotron X-ray data (pseudo-Voigt).