Fourier Methods
An Introduction to the Fourier Transform JCE
Scott Van Bramer, Widener University
This document simultaneously introduces students to how the Fourier transform works and how various instrument parameters affect the results of the Fourier transform. Waveforms are produced and integrated using sine waves, cosine waves, and simple functions. The fast Fourier transform is used with simulated data to introduce students to the relationship between the signal waveform and the signal frequency of a spectrum. Students are then led to the concepts of dwell time and resolution through a series of interactive exercises. The document ends with an introduction to the Fourier transform of decaying signals. Students and teachers may use IntroFourierTransform.mcd as written, or teachers may remove some graphs to increase discovery learning and class discussion.
Exploring Fourier Transform Techniques with Mathcad JCE
Mark Iannone, Millersville University
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. The entire set of documents contains many student exercises and hands-on activities for learning the concepts presented.
Fourier Transforms of Molecular Vibrations JCE
W. Tandy Grubbs, Stetson University
This series of three Mathcad instructional documents permits students to explore the relationship between the time and frequency representations of vibrational motion in simple diatomic molecules. Exercises included throughout and at the end of each document allow students to practice the numerical methods and further investigate how bond anharmonicity and vibrational damping affect the frequency spectrum.
Introductory Explorations of the Fourier Series JCE
Theresa Julia Zielinski, Monmouth University
A Mathcad template that provides students with quided inquiry practice using a Fourier series expansion.
Studies in FT-IR
Scott Van Bramer, Widener University
This is a collection of six documents that can be used to teach and learn the basic concepts of FT-IR. ft_notes.mcd, provides an introduction to FT as a lecture handout or interactive student activity. In ft_01_6.mcd students study the parameters that affect resolution and spectral width. ft_02_06.mcd shows how two frequency components add to give a beat pattern. ft_03_6.mcd shows how cosine and sine waves describe the frequency and phase of a signal. In ft_04_6.mcd students examine the effect of an exponential decay in the time domain and frequency domain. The entire series of documents is summarized in ft_05_6.mcd which contains large fonts and no explanatory text and is designed for use in class lectures.