Using Discrete Fourier Transforms to Create Artistic Visuals

Abstract

Fourier transforms are a fundamental component of modern techniques due to their wide applications in our digital world. One of the most essential applications of Fourier series is the approximation of periodic functions using trigonometric polynomials. Through this method, closed curves can be traced by manipulating a system of rotating orbits. Fourier transforms are extensively used in signal and sound analysis, as well as in physics and applied mathematics. In this paper, Python programming language was employed to generate animated artistic visuals through rotating orbits, providing a simplified visual demonstration of Fourier transforms. This approach aims to facilitate understanding by merging art with programming.