Figurative Lissajous: Lissajous Figures Classification Model

In this work, we built, trained, and tested neural networks to identify and classify Lissajous Figures corresponding to commensurate frequency ratios, widely used in signal processing, instrument calibration, and fault diagnostics. For instance, Lissajous Figures can be employed to determine the frequency of an unknown signal by comparing it with a reference signal of known frequency. Simple sequential convolutional models were developed, comprising three convolution layers, two pooling layers, and several dense layers. Each model weighs under 200 MB, enabling execution on low-end hardware. The models were implemented in Python using TensorFlow and NumPy. The training dataset consisted of ≈1200 experimentally acquired images from a Digital Storage Oscilloscope (DSO) in an undergraduate laboratory setup. Evaluation was performed on ≈500 experimental DSO images and ≈2200 images with simulated noise in Python, achieving over 99 % accuracy on experimental data and above 93 % on simulated data, demonstrating strong generalization across both domains. The work holds pedagogical value in undergraduate physics education by integrating experimental and computational skills, and its low hardware demands make it ideal for classroom and project-based learning.