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Title: Discrete wavelets on $\mathbb{Z}_N$
Author: Debernardi Pinos, Alberto
Director/Tutor: Soria de Diego, F. Javier
Keywords: Ondetes (Matemàtica)
Anàlisi de Fourier
Tesis de màster
Wavelets (Mathematics)
Fourier analysis
Masters 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
Appears in Collections:Màster Oficial - Matemàtica Avançada

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