Generalized Sampling: From Fourier to Wavelet

Student thesis: Master thesis (including HD thesis)

  • Josefine Holm
  • Steffen L√łnsmann Nielsen
4. semester, Mathematical Engineering, Master (Master Programme)
In this project we investigate generalized sampling as a tool for signal reconstruction and compression. Generalized sampling is a relatively new method for recovering any element in a finite dimensional space given finitely many samples in an arbitrary frame. The focus is on Fourier frames as sampling space and Daubechies wavelets as reconstruction space. We investigate the subject both in theory and in practise by proving relevant theorems and implementing algorithms in Python. Most of the theory is already published by others. However, to the best of our knowledge, it has not been implemented in Python before. The method is tested on several different signals with overall positive results. Among the test signals are both continuous and discontinuous signals, signals in one and two dimensions, and uniformly and nonuniformly sampled signals. For most of the tested signals compression using generalized sampling results in smaller errors than compression directly in the Fourier frame.
LanguageEnglish
Publication date2018
Number of pages93
ID: 280490229