Interactive Tools for Teaching Fourier Transforms

Carlos R. Baiz
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引用次数: 3

Abstract

Fourier transforms (FT) are universal in chemistry, physics, and biology. Despite FTs being a core component of multiple experimental techniques, undergraduate courses typically approach FTs from a mathematical perspective, leaving students with a lack of intuition on how an FT works. Here, I introduce interactive teaching tools for upper-level undergraduate courses and describe a practical lesson plan for FTs. The materials include a computer program to capture video from a webcam and display the original images side-by-side with the corresponding plot in the Fourier domain. Several patterns are included to be printed on paper and held up to the webcam as input. During the lesson, students are asked to predict the features observed in the FT and then place the patterns in front of the webcam to test their predictions. This interactive approach enables students with limited mathematical skills to achieve a certain level of intuition for how FTs translate patterns from real space into the corresponding Fourier space.
傅立叶变换交互式教学工具
傅立叶变换(FT)在化学、物理学和生物学中是普遍的。尽管FT是多种实验技术的核心组成部分,但本科生课程通常从数学角度来处理FT,这让学生对FT的工作方式缺乏直觉。在这里,我介绍了高水平本科课程的互动教学工具,并描述了一个实用的FT课程计划。这些材料包括一个计算机程序,用于从网络摄像头捕捉视频,并在傅立叶域中与相应的绘图并排显示原始图像。有几个图案被打印在纸上,并被举到网络摄像头作为输入。在课程中,学生被要求预测在FT中观察到的特征,然后将这些模式放在网络摄像头前,以测试他们的预测。这种交互式方法使数学技能有限的学生能够获得一定程度的直觉,了解FT如何将模式从真实空间转换到相应的傅立叶空间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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