Related Experiment Video
Updated: Mar 26, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
Published on: August 19, 2021
Functional mixed effects spectral analysis
Robert T Krafty1, Martica Hall2, Wensheng Guo3
1Department of Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A. krafty@pitt.edu.
Abstract:
In many experiments, time series data can be collected from multiple units and multiple time series segments can be collected from the same unit. This article introduces a mixed effects Cramér spectral representation which can be used to model the effects of design covariates on the second-order power spectrum while accounting for potential correlations among the time series segments collected from the same unit. The transfer function is composed of a deterministic component to account for the population-average effects and a random component to account for the unit-specific deviations. The resulting log-spectrum has a functional mixed effects representation where both the fixed effects and random effects are functions in the frequency domain. It is shown that, when the replicate-specific spectra are smooth, the log-periodograms converge to a functional mixed effects model. A data-driven iterative estimation procedure is offered for the periodic smoothing spline estimation of the fixed effects, penalized estimation of the functional covariance of the random effects, and unit-specific random effects prediction via the best linear unbiased predictor.
Related Concept Videos
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations
Mass Spectrometry: Complex Analysis
GC–MS is a powerful hyphenated method commonly used in forensics and environmental...
¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)
Aliasing
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
¹H NMR Signal Multiplicity: Splitting Patterns

