This article explains how the Fourier transform can be used to draw complex shapes by combining rotating circles (epicycles) at different frequencies, radii, and phases. The technique is demonstrated with examples like drawing a llama using 1024 circles, and the article introduces the mathematical foundations including complex numbers and frequency domain analysis.
These notes explain discrete-time Fourier series (DTFS) and the discrete-time Fourier transform (DTFT), which are fundamental to digital signal processing. The content covers periodic discrete signals represented as linear combinations of complex exponentials, methods for calculating Fourier coefficients, and includes a worked example using a sampled triangular function with 12 samples per period.