JCE
Exploring Fourier Transform Techniques with Mathcad©
Mark Iannone
Department of Chemistry
Millersville University
Millersville, PA 17551
USA
mail to: miannone@marauder.millersv.edu



Abstract
These four Mathcad documents illustrate different aspects of the Fourier transform. They explore the source of the Nyquist frequency and the dependence of the resolution of the spectrum on sampling. In FTIntro.mcd, students achieve a qualitative understanding of the Fourier transform through experimentation with graphic representations of data and their transforms. In Part 1 of FTIntro.mcd, students sample a continuous function and learn how aliasing can occur; in Part 2, a vector of a more complex waveform illustrates that the frequencies contained in the waveform appear as spectral lines in the transform. Exercises permit further exploration of the Nyquist frequency and illustrate the relationship of resolution to number of samples. At the end, the students perform an integral transform of the same waveform. The second document, FT2IR.mcd, demonstrates how spectral information is coded in an interferogram and how the interferometric data limits resolution in the spectrum. In FT2IR.mcd, the inverse FT is used to generate an interferogram from a spectrum with two notches representing absorption. The third document, FT3Pulse.mcd, demonstrates that a short sample of a wave must contain a range of frequencies. In the fourth document, FT4FreeIndDecay.mcd, free induction decay (FID) and its Fourier transform are explored and related to NMR signal analysis. The entire set of documents contains many student exercises and hands-on activities for learning the concepts presented.
Commentary
Editor's Commentary
Keywords
Audiences: Upper-Division Undergraduate
Pedagogies: Computer-Based Learning
Domains: Analytical Chemistry, Laboratory Instruction, Physical Chemistry
Topics: Fourier Transform Techniques, Mathematics / Symbolic Mathematics, NMR Spectroscopy
Documents
File NameDescriptionSoftware TypeSoftware Version
FourierNotes.pdf Instructor Notes
FT2IR.mcd JCE Mathcad Computational Document Mathcad
FT2IR.pdf Read-Only Document
FT3Pulse.pdf Read-Only Document
FT4FreeIndDecay.pdf Read-Only Document
FTIntro.pdf Read-Only Document
FT3Pulse.mcd JCE Mathcad Computational Document Mathcad
FT4FreeIndDecay.mcd JCE Mathcad Computational Document Mathcad
FTIntro.mcd JCE Mathcad Computational Document Mathcad
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Citations
Iannone, M. J. Chem. Educ. 1999, 76, 286.
Comments to: Mark Iannone at miannone@marauder.millersv.edu
©Copyright 1998 by the Division of Chemical Education, Inc., American Chemical Society. All rights reserved. For classroom use by teachers, one copy per student in the class may be made free of charge. Write to JCE Online, jceonline@chem.wisc.edu, for permission to place a document, free of charge, on a class Intranet.