Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

4.7K
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
4.7K
Root Mean Square00:57

Root Mean Square

4.0K
If in an experiment, data values have a probability of being both positive and negative, neither the arithmetic mean, the geometric mean, nor the harmonic mean can be used to calculate the central tendency of the data set. In particular, if the positive and negative values are equally likely, the arithmetic mean is close to zero.
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...
4.0K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

412
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
412
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

9.7K
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
9.7K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

387
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
387
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

2.0K
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
2.0K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Determining 3D molecular orientation from polarization-IR spectra: tutorial.

Journal of the Optical Society of America. A, Optics, image science, and vision·2025
Same author

Solvent Exclusion Effect on Infrared Absorption Spectroscopy.

Analytical chemistry·2025
Same author

Benchtop IR Imaging of Live Cells: Monitoring the Total Mass of Biomolecules in Single Cells.

Analytical chemistry·2024
Same author

Quantum Cascade Laser Infrared Spectroscopy for Glycan Analysis of Glycoprotein Solutions.

Analytical chemistry·2024
Same author

Single-detector double-beam modulation for high-sensitivity infrared spectroscopy.

Scientific reports·2023
Same author

3D Orientation Imaging of Polymer Chains with Polarization-Controlled Coherent Raman Microscopy.

Journal of the American Chemical Society·2022
Same journal

EXPRESS: Deterministic Compressed Sensing in Time-Domain Spectroscopy.

Applied spectroscopy·2026
Same journal

EXPRESS: Multi-Parameter Wavelength Characterization of Array Spectrometers Under Near-Limit Sampling Conditions.

Applied spectroscopy·2026
Same journal

EXPRESS: A Validated Reference Database for Twentieth-Century Cd-Based Pigments: Integrated Structural and Compositional Characterization.

Applied spectroscopy·2026
Same journal

EXPRESS: Two-Trace Two-Dimensional (2T2D-COS) in the Analysis of Brain Tissue Sample Preparation Method.

Applied spectroscopy·2026
Same journal

EXPRESS: Simplified Protocol for Analyzing Polarization Properties of Scanning Tunneling Microscope (STM) Light Emission Spectra at an Oblique Angle.

Applied spectroscopy·2026
Same journal

EXPRESS: Monitoring a Polyurethane Synthesis by Fiber-Coupled Attenuated Total Reflection Fourier Transform Infrared Spectroscopy and Multivariate Curve Resolution-Alternating Least Squares.

Applied spectroscopy·2026
See all related articles

Related Experiment Video

Updated: Mar 8, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.1K

Least Squares Moving-Window Spectral Analysis.

Young Jong Lee1

  • 1Biosystems & Biomaterials Division, National Institute of Standards and Technology, Gaithersburg, MD, USA.

Applied Spectroscopy
|January 21, 2017
PubMed
Summary
This summary is machine-generated.

Least squares moving-window (LSMW) regression offers a novel approach for analyzing spectral data affected by external perturbations. This method effectively handles nonuniform spacing and high-frequency noise in spectral analysis.

Keywords:
Least squares moving-window regressionSavitzky–Golay numerical differentiationtwo-dimensional correlation spectroscopy

More Related Videos

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

618
A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

9.0K

Related Experiment Videos

Last Updated: Mar 8, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.1K
A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

618
A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

9.0K

Area of Science:

  • Spectroscopy
  • Chemometrics
  • Data Analysis

Background:

  • Spectral data analysis often faces challenges with nonuniformly spaced data and noise.
  • Existing numerical differentiation methods may not be optimal for complex spectral datasets.

Purpose of the Study:

  • To introduce and evaluate the Least Squares Moving-Window (LSMW) method for spectral data analysis.
  • To demonstrate LSMW's effectiveness in handling nonuniform perturbation spacing and high-frequency noise.

Main Methods:

  • Least squares regression applied as a moving-windows technique.
  • Characterization of LSMW based on window size, perturbation spacing, and noise levels.
  • Comparison with single-interval differentiation, autocorrelation moving-window, and perturbation correlation moving-window methods.

Main Results:

  • LSMW is presented as an extension of Savitzky-Golay differentiation for nonuniform spacing.
  • Simulation results show LSMW's performance characteristics.
  • LSMW demonstrates utility in quantitative analysis of noisy, nonuniformly spaced spectral data.

Conclusions:

  • The LSMW method provides a robust and simple approach for spectral data analysis.
  • LSMW is particularly advantageous for quantitative analysis of spectral series with high-frequency noise and irregular sampling.