Projects for the UW AMATH 582 Computational Methods For Data Analysis class
Detecting objects through frequency signatures
A Kraken’s trajectory was estimated using noisy acoustic data with an unknown characteristic frequency. The spatial frequency and location of the submarine in 3D space were determined using Fourier analysis and filtering in Python. There was a significant improvement when the results were compared before and after filtering.
Parsing musical frequency signatures
This project explores the application of the Gabor Transform, a fundamental signal analysis technique, to analyze the sound clip provided and extract time-frequency information. Using discrete window sampling, spectrograms were created in Python, and frequency filtering was employed to isolate the baseline and guitar melody in the clips.
Principal Component Analysis of a Mass-on-a-spring System
Data from three different camera angles were used to evaluate the motion of a mass (a paint can) on a spring using principal component analysis and image processing techniques. Thresholds were utilized to isolate and track the paint can, and image stabilization was used to smooth the transitions between frames. The weighting of each component in the transformation matrix was established using singular value decomposition (SVD) techniques.
Teaching a Computer to Recognize Written Numbers
This project focuses on training a computer to recognize written numbers using a subset of Yann LeCun’s dataset. It aims to develop a system capable of accurately identifying written numbers, which can have various applications in fields such as image recognition and computer vision.
Background Subtraction through Dynamic Mode Decomposition
The aim of the study was to use Dynamic Mode Decomposition (DMD) to subtract the background variations in order to analyze the temporal dynamics of a moving object in the video clip and extract its spatiotemporal patterns.