Classroom activities are needed that provide students hands-on experience utilizing Fourier techniques. Modern pedagogical approaches are designed to develop competency across the entire cognitive spectrum: Remembering, Understanding, Applying, Analyzing, Evaluating, and Creating ( 14). Thus, it is challenging for students not equipped with strong mathematical skills to understand what a FT does and, more so, to acquire intuition for how a FT translates one function into its conjugate function in the Fourier domain. Although there are many excellent articles and textbooks on Fourier methods, pedagogical approaches can be highly mathematical ( 9– 11), introduced within the context of specific techniques ( 12), or be brief and oversimplified ( 13). Developing an intuitive understanding of FTs is therefore essential for undergraduate students to fully grasp the principles behind these techniques. Although certain experimental methods, such as infrared spectroscopy, are nearly universal in undergraduate teaching laboratories, FTs are automatically carried out by internal software libraries with preprogrammed settings that are typically hidden from the user ( 8). Modern molecular dynamics simulation packages implement fast FT algorithms to improve computational accuracy and efficiency ( 7). Spatial reconstruction algorithms based on FTs are at the core of modern biomedical imaging applications, such as magnetic resonance imaging ( 6). Biophysical characterization techniques, including nuclear magnetic resonance (NMR) spectroscopy ( 1), infrared spectroscopy ( 2), x-ray crystallography ( 3), mass spectrometry ( 4), and differential scanning calorimetry, rely on FTs for data processing or analysis ( 5). 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.įourier Transforms (FTs) are an essential mathematical tool for numerous experimental and theoretical methods. 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.
![fourier transform graphed complex coordinate system fourier transform graphed complex coordinate system](https://image.slidesharecdn.com/fouriertransform-140924230100-phpapp02/95/fourier-transform-12-638.jpg)
Several patterns are included to be printed on paper and held up to the webcam as input. 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. Here, I introduce interactive teaching tools for upper-level undergraduate courses and describe a practical lesson plan for FTs. 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. Fourier transforms (FT) are universal in chemistry, physics, and biology.