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Innovative Teaching Of Fourier Series Using Labview

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Conference

2006 Annual Conference & Exposition

Location

Chicago, Illinois

Publication Date

June 18, 2006

Start Date

June 18, 2006

End Date

June 21, 2006

ISSN

2153-5965

Conference Session

Use of Technology in Teaching Mathematics

Tagged Division

Mathematics

Page Count

13

Page Numbers

11.771.1 - 11.771.13

Permanent URL

https://peer.asee.org/415

Download Count

505

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Paper Authors

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Peter Avitabile University of Massachusetts-Lowell

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Peter Avitabile is an Associate Professor in the Mechanical Engineering Department and the Director of the Modal Analysis and Controls Laboratory at the University of Massachusetts Lowell. He is a Registered Professional Engineer with a BS, MS and Doctorate in Mechanical Engineering and a member of ASEE, ASME and SEM.

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Jeffrey Hodgkins University of Massachusetts-Lowell

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Jeff Hodgkins is a Graduate Student in the Mechanical Engineering Department at the University of Massachusetts. He is currently working on his Master’s Degree in the Modal Analysis and Controls Laboratory while concurrently working on the NSF Engineering Education Grant.

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Tracy Van Zandt University of Massachusetts-Lowell

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Tracy Van Zandt is a Graduate Student in the Mechanical Engineering Department at the University of Massachusetts. She is currently working on her Master’s Degree in the Modal Analysis and Controls Laboratory while concurrently working on the NSF Engineering Education Grant.

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Abstract
NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

INNOVATIVE TEACHING OF FOURIER SERIES USING LABVIEW

Abstract

Students often “glaze over” when detailed mathematical derivations are presented in class. Fourier series, the Fourier Integral and the FFT pose some significant mathematical derivations that can put any student to sleep – integrals, orthogonal functions and so on are only glamorous to the professor who relishes their derivation. However, the basic utilization of the Fourier series and FFT are very important to many applications. An understanding of their use is critical to a student’s success in several different applications such as harmonic analysis, time and frequency response, and filtering.

A lab exercise using LabVIEW is developed to demonstrate Fourier series and the FFT process along with harmonics and filtering. The students develop a graphical user interface (GUI) using LabVIEW to process simple sinusoidal signals, sum sine waves to approximate general signals (such as a square wave), take Fourier transforms, and present data in the time and frequency domain. Graphical controls (sliders or level gain) are used for both frequency and amplitude of the individual summed sine waves. The students are tasked to generate various types of waveforms and then compare the time and frequency outputs to assess the truncation of the series developed; the coefficients are then compared to the widely published Fourier series coefficients for each of the signals.

Without requiring a rigorous mathematical development, the students gain first hand appreciation of the Fourier transformation process from a very intuitive, graphical process and, at the same time, learn important features of the LabVIEW software program. The assigned project allows the students to develop their own interface with the features that are intuitive to themselves rather than using a “canned” GUI to illustrate the Fourier series process. Tutorial material describing LabVIEW overview and individual tools needed are presented in class and available as voice annotated Flash file overview. Students have used both “canned” MATLAB GUIs and standard laboratory exercises using an actual FFT analyzer with signals generated by a function generator to observe the same phenomena. The students have overwhelmingly indicated that the individual development of the Fourier transformation via LabVIEW was a much better learning experience. The project, the results and students’ observations are presented.

I. Problem

Students need to apply mathematical concepts with a firm, rooted understanding of the tools that are employed. The application of Fourier Series, spectral processing, the Fast Fourier Transform and concepts of filtering need to be well understood for a wide variety of applications. The traditional approach of mathematical development of equations with homework and test problems does not appear to drive the students to learn the material for any particular reason. Implementation of laboratory exercises with lab based FFT analyzers end up causing students to

Avitabile, P., & Hodgkins, J., & Van Zandt, T. (2006, June), Innovative Teaching Of Fourier Series Using Labview Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. https://peer.asee.org/415

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