Please use this identifier to cite or link to this item:
https://dipositint.ub.edu/dspace/handle/2445/63187
Title: | Discrete wavelets on $\mathbb{Z}_N$ |
Author: | Debernardi Pinos, Alberto |
Director/Tutor: | Soria de Diego, F. Javier |
Keywords: | Ondetes (Matemàtica) Anàlisi de Fourier Treballs de fi de màster Wavelets (Mathematics) Fourier analysis Master's theses |
Issue Date: | Jun-2014 |
Abstract: | This Master’s thesis is devoted to develop the theory of discrete (finite-dimensional) wavelets. In this context, wavelets are very concrete basis of vectors with special properties that make them suitable for the purpose of data compressing or digital signal processing, among others. Thus, this will be our ultimate goal in the study of wavelets. Since we are considering finite-dimensional vectors, the whole theory is based in linear algebraic techniques. This theory can also be extended for vectors in $\mathbb{Z}$, and for functions in $\MATHBB{R}$; actually, there will be several analogies between these different settings that will be remarked throughout the work. In fact, this theory was firstly studied in $\mathbb{R}$, being [10] and [11] its predecessors. After introducing the main results in the discrete setting, we also give several examples of data compression. Surprisingly, wavelets will allow us to reduce significantly the amount of information needed to reproduce a vector (or a matrix), which is very important for data storage and transmission, since the less information we need, the less resources we have to use. |
Note: | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2014, Director: F.Javier Soria de Diego |
URI: | http://hdl.handle.net/2445/63187 |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
memoria.pdf | Memòria | 1.29 MB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License