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 Name Description Software Type Software Version FourierNotes.pdf Instructor Notes FT2IR.mcd 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 Mathcad Computational Document Mathcad FT4FreeIndDecay.mcd Mathcad Computational Document Mathcad FTIntro.mcd Mathcad Computational Document Mathcad JCE Subscribers only: name and password or institutional IP number access required.
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.