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# Fourier Series Approximation GUI PowerPoint PPT Presentation

Fourier Series Approximation GUI. Stephen McMillan and Irina Ramanandraitsiory “ Mathematical Analysis is as extensive as nature herself.” -Joseph Fourier. Joseph Fourier. French mathematician (21 March 1768 – 16 May 1830)

Fourier Series Approximation GUI

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## Fourier Series Approximation GUI

Stephen McMillan and Irina Ramanandraitsiory

“Mathematical Analysis is as extensive as nature herself.”

-Joseph Fourier

### Joseph Fourier

• French mathematician (21 March 1768 – 16 May 1830)

• One of his most noteworthy achievements was the formulation of the Fourier Series.

• Alongside his mathematical contributions he is credited as the first to propose the concept of the greenhouse effect.

### The Fourier Series

• A mathematical tool used to decompose any arbitrary periodic signal or function into a possibly infinite set of simple sine and cosine functions.

• Originally discovered to help Fourier with the heat equation in a metal plate.

• Developed off of former work done by Leonhard Euler, Daniel Bernoulli, and others on trigonometric series.

- James Stewart

### Our Goal

• Make an educational labview GUI that allows the user to experiment with the Fourier Series in order to gain an understanding of its power and usefulness.

### GUI Features

• Allows the user to try and approximate a square, triangle, or saw tooth wave (of any amplitude and frequency) by modifying the amplitude and frequency of 5 sine waves.

• Plots each modification in real time.

• Shows the time response and the frequency response.

• Shows the effects of a low pass filter and a band pass filter.

• Allows for automatic approximations in case the user has trouble finding the correct amplitudes and frequencies.

Front Panel

### Example (cont.)

Time Response of the Summed Sine Waves

### Example (cont.)

Frequency Response of the Summed Sine Waves

### Example (cont.)

Effect of the Low Pass Filter on the Summed Sine Waves

### Example (cont.)

Effect of the Band Pass Filter on the Summed Sine Waves

### Applications of the Fourier Series

• Led to the development of the Fourier Transform which decomposes non-periodic function.

• Used in file compression such as JPEG image format.

• Used in signal processing in communications and astronomy, acoustics, optics, and cryptography.

### Sources

• http://ocw.mit.edu/courses/mathematics/18-100c-analysis-i-spring-2006/projects/niu.pdf

• http://en.wikipedia.org/wiki/Fourier_series

• http://www.stewartcalculus.com/data/CALCULUS%20Early%20Transcendentals/upfiles/FourierSeries5ET.pdf

• https://kiwi.ecn.purdue.edu/rhea/index.php/ECE_301_Fall_2007_mboutin_Definitions

• http://strangewondrous.net/browse/author/f/fourier+joseph