Detail publikace

# Discrete Wavelet Transform of Finite Signals: Detailed Study of the Algorithm

Originální název

Discrete Wavelet Transform of Finite Signals: Detailed Study of the Algorithm

Anglický název

Discrete Wavelet Transform of Finite Signals: Detailed Study of the Algorithm

Jazyk

en

Originální abstrakt

The paper presents a detailed analysis of algorithms used for the forward and the inverse discrete wavelet transform (DWT) of finite-length signals. The paper provides answers to questions such as "how many wavelet coefficients are computed from the signal at a given depth of the decomposition" or conversely, "how many signal samples are needed to compute a single wavelet coefficient at a given depth of the decomposition" or "how many coefficients at a given depth are influenced by the selected type of boundary treatment" or "how many samples of the input signal simultaneously influence two neighboring wavelet coefficients at a given depth of the decomposition". As a byproduct, the rigorous analysis of the algorithms gives details needed for the implementation. The paper is accompanied by several Matlab functions.

Anglický abstrakt

The paper presents a detailed analysis of algorithms used for the forward and the inverse discrete wavelet transform (DWT) of finite-length signals. The paper provides answers to questions such as "how many wavelet coefficients are computed from the signal at a given depth of the decomposition" or conversely, "how many signal samples are needed to compute a single wavelet coefficient at a given depth of the decomposition" or "how many coefficients at a given depth are influenced by the selected type of boundary treatment" or "how many samples of the input signal simultaneously influence two neighboring wavelet coefficients at a given depth of the decomposition". As a byproduct, the rigorous analysis of the algorithms gives details needed for the implementation. The paper is accompanied by several Matlab functions.

Dokumenty

BibTex

``````
@article{BUT103244,
author="Pavel {Rajmic} and Zdeněk {Průša}",
title="Discrete Wavelet Transform of Finite Signals: Detailed Study of the Algorithm",
annote="The paper presents a detailed analysis of algorithms used for the forward and the inverse discrete wavelet transform (DWT) of finite-length signals. The paper provides answers to questions such as "how many wavelet coefficients are computed from the signal at a given depth of the decomposition" or conversely, "how many signal samples are needed to compute a single wavelet coefficient at a given depth of the decomposition" or "how many coefficients at a given depth are influenced by the selected type of boundary treatment" or "how many samples of the input signal simultaneously influence two neighboring wavelet coefficients at a given depth of the decomposition". As a byproduct, the rigorous analysis of the algorithms gives details needed for the implementation. The paper is accompanied by several Matlab functions.",
address="World Scientific Publishing Company",
chapter="103244",
doi="10.1142/S0219691314500015",
howpublished="online",
institution="World Scientific Publishing Company",
number="1",
volume="12",
year="2014",
month="january",
pages="1450001-1--1450001-38",
publisher="World Scientific Publishing Company",
type="journal article in Web of Science"
}``````