| dc.contributor.author | Ssegawa, Yasini | |
| dc.date.accessioned | 2023-01-06T12:37:26Z | |
| dc.date.available | 2023-01-06T12:37:26Z | |
| dc.date.issued | 2022-12-12 | |
| dc.identifier.citation | Ssegawa, Y. (2022). On the Wavelet Analysis of Square Integrable Functions. (Makir). (Unpublished Masters thesis). Makerere University, Kampala, Uganda. | en_US |
| dc.identifier.uri | http://hdl.handle.net/10570/11337 | |
| dc.description | A dissertation submitted to the Directorate of Research and Graduate Training in partial ful lment of the requirements for the Award of the Degree of Master of Science in Mathematics of Makerere University. | en_US |
| dc.description.abstract | In this study, we derive the conditions under which an arbitrary L^2(R) function can be expanded in terms of the wavelet basis. This is done by rst deriving the conditions under which an arbitrary scaling function and the subspaces Vj form a multiresolution analysis for the L^2(R) space. Speci c examples like the Haar multiresolution analysis and the Meyer multiresolution analysis have been constructed using the Haar scaling function and the Meyer scaling function respectively. Furthermore, we derive conditions under which the set of wavelet functions form an orthonormal wavelet basis for the subspaces Wj . Examples such as the Haar wavelet and the Meyer wavelets have been constructed to span the L^2(R) space. Lastly, we demonstrate the approximation and smoothening of L^2(R) functions using discrete wavelets. | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Makerere University. | en_US |
| dc.subject | Wavelets, | en_US |
| dc.subject | Square integrable. | en_US |
| dc.title | On the Wavelet Analysis of Square Integrable Functions. | en_US |
| dc.type | Thesis | en_US |
