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Related Concept Videos

Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
IR Frequency Region: Fingerprint Region01:03

IR Frequency Region: Fingerprint Region

IR spectra are divided into two main regions: the diagnostic region and the fingerprint region. The diagnostic region of the spectrum lies above 1500 cm−1. The absorptions resulting from single-bond vibrations of the N–H, C–H, and O–H stretch at higher wavenumbers and appear on the left side of the spectrum. The stretching absorptions of the C≡C and C≡N occur between 2100–2300 cm−1. In contrast, those arising from stretching absorptions of the C=O, C=N, and C=C occur between 1600–1850 cm−1.
The...
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...
UV–Vis Spectroscopy: Woodward–Fieser Rules01:29

UV–Vis Spectroscopy: Woodward–Fieser Rules

UV–Visible absorption spectra of conjugated dienes arise from the lowest energy π → π* transitions. The light-absorbing part of the molecule is called the chromophore, and the substituents directly attached to the chromophore are called auxochromes. A strong correlation exists between the absorption maxima, λmax, and the structure of a conjugated π system. The Woodward–Fieser rules predict the value of λmax for a given structure by adding the contributions...
IR Spectroscopy: Molecular Vibration Overview01:24

IR Spectroscopy: Molecular Vibration Overview

When Infrared (IR) radiation passes through a covalently bonded molecule, the bonds transition from lower to higher vibrational levels. The fundamental vibrational motions that result in infrared absorption can be classified as stretching or bending vibrations.
Stretching vibrations are vibrational motions that occur along the bond line, changing the bond length or distance between two bonded atoms. They are further distinguished as symmetric or asymmetric. In symmetric stretching, the...
Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...

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Related Experiment Video

Updated: May 16, 2026

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

Published on: August 19, 2021

[FTIR spectral fitting algorithm based on continuous wavelet transform].

An Jiang1, Jiang-Tao Peng, Huai-Song Wang

  • 1School of Management Science & Engineering, Nanjing University of Finance & Economics, Nanjing 210046, China. an.jiang@ia.ac.cn

Guang Pu Xue Yu Guang Pu Fen Xi = Guang Pu
|December 18, 2012
PubMed
Summary
This summary is machine-generated.

A new algorithm using continuous wavelet transform (CWT) improves Fourier Transform Infrared (FTIR) spectral subtraction. This method accurately quantifies liquor content, overcoming limitations of existing software.

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Area of Science:

  • Analytical Chemistry
  • Spectroscopy
  • Signal Processing

Context:

  • Fourier Transform Infrared (FTIR) spectroscopy is a powerful analytical technique.
  • Traditional FTIR spectral subtraction methods often struggle with reference peak and manual factor selection.
  • Developing robust algorithms for accurate spectral analysis is crucial.

Purpose:

  • To propose a novel FTIR spectrum fitting algorithm utilizing continuous wavelet transform (CWT).
  • To address the limitations of conventional spectral subtraction techniques in commercial software.
  • To evaluate the performance of CWT-based spectral fitting for quantitative analysis.

Summary:

  • The proposed algorithm integrates original FTIR spectra with their CWT-transformed counterparts to calculate difference spectra.
  • This approach effectively bypasses the need for manual reference peak and factor selection.
  • Spectral fitting was performed using six wavelet basis functions, yielding scale factors for liquor content quantification with low mean absolute error (0.047–0.072) and standard deviation (0.056–0.091).

Impact:

  • Introduces an accurate and reliable method for FTIR spectral subtraction.
  • Demonstrates the utility of CWT combined with least squares fitting for quantitative analysis.
  • Offers a potential advancement for spectral data processing in various scientific applications.