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Fourier Transforms, Fourier Series and the FFT
Lesette de Pillis
Harvey Mudd College
depillis@hmc.edu |
Amy Radunskaya
Pomona College
Ami_Radunskaya@pomona.edu |
Introduction: This module on Fourier Transforms
is ideally introduced in a course on modeling or on scientific computing,
or as enrichment for an introductory course in linear algebra, honors
calculus, or engineering. It is self-contained and presented from
an introductory perspective.
Module Objectives: The objectives of this module
include providing the students with an introductory level of familiarity
with the Fourier Transform that will allow them to:
• Recognize mathematical and physical situations in which
the Fourier Transform may be useful for analysis.
• Understand when it is appropriate to use a Continuous Fourier
Transform, and when one should use a Discrete Fourier Transform.
• Understand the connection between the Continuous Fourier
Transform, the Fourier Series, and the Discrete Fourier Transforms.
• Understand how numerically to apply a Fourier Transform
to a set of data, and what the resulting transform represents.
• Be familiar with packaged Fourier Transform routines (we
use MATLAB routines) and be able to use them with understanding.
• Understand computational efficiency issues of the Fourier
Transform.
• Discuss and assess Fourier Transform results.
Overview document. Overview.pdf
(3 pages)
Introduction to Fourier Transforms: Instructor slides with notes.
Intro.pdf (57 pages)
Introduction to Fourier Transforms: Presentation slides. IntroSlidesOnly.pdf
(71 pages)
Introduction to Fourier Transforms: Student handout slides: IntroSlidesHandouts.pdf
(36 pages)
Fourier Transform exercises. FFTExercises.pdf
(10 pages)
Matlab demonstration scripts and supporting files. We suggest saving
these files directly to your hard-drive.
DoSpectrum.m
NoisyAh.mat
SingingAh.mat
co2dat.m
co2FFT.m
CO2demo.txt
FFTtimingsDemo.m
For more information, please contact
Ignatios Vakalis (614-236-6587)
Principle Investigator
Andrea Karkowski (614-236-6449)
Co-PI
Terry Lahm (614-236-6800)
Co-PI
Susan Stumpp Grant Administrator
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