Peak Retention Time Using Discrete Fourier Transform

Consider a noise-free signal (e.g. a chromatogram of two chemical species), for instance, the sum of two Gaussian functions. This signal is given by , where the user can set the values of parameters , , , and . These two Gaussian functions can show partial or even complete overlap.
The blue curve shows the original signal. In this plot, there are either three extrema (two peaks shown in red and one valley shown in green) or only one extremum (one peak shown in red), when the two Gaussian functions overlap sufficiently.
This Demonstration applies the discrete Fourier transform to compute the derivative of the signal . This derivative is shown by the red curve. In addition, the positions of the extrema of are indicated by the blue dots in the derivative plot. A list of these extrema is given using the "peaks" tab. Clearly, for a valley, and , and for peaks, and .
Similar calculations are also possible for real signals, which may have white noise. Choose the "noisy chromatogram" tab to see the results for one particular case.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+