The Mystery Curve: A Signal Processing Point of View [Lecture Notes]
In the first chapter of a recently published book on artful mathematics [1], a linear combination of harmonic signals called mystery curves were introduced. Although their Fourier-based analysis brings interesting results, this lecture note provides a different and important perspective, especially useful for our signal processing community. Based on polar coordinate systems and low-pass filtering approaches, the patterns of the curves can be designed by locally curve tracing instead of trial and error, including not only two-dimensional (2-D) but also three-dimensional (3-D) modeling. Concrete examples and online MATLAB codes are provided so that applications from art and logo design to amplitude modulation (AM)-frequency modulation (FM) signal analysis are realizable.