Generalized Sampling: From Fourier to Wavelet

Studenteropgave: Speciale (inkl. HD afgangsprojekt)

  • Josefine Holm
  • Steffen Lønsmann Nielsen
4. semester, Matematik-teknologi, Kandidat (Kandidatuddannelse)
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.
SprogEngelsk
Udgivelsesdato2018
Antal sider93
ID: 280490229