An Analysis of Stockwell Transforms, with Applications to Image Processing
John Ladan · UWSpace (University of Waterloo) · 2014
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Time-frequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the Short-Time Fourier Transform (or Gabor transform). In 1996 the Stockwell transform was introduced to maintain the phase of the Fourier transform, while also providing the progressive resolution of the wavelet transform. The discrete orthonormal Stockwell transform is a more efficient, less redundant transform with the same properties. There has been little work on mathematical properties of the Stockwell transform, particularly how it behaves under operations such as translation and modulation. Previ-ous results do discuss a resolution of the identity, as well as some of the function spaces that may be associated with it [2]. We extend the resolution of the identity results, and