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

journal article in Web of Science

English

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.

DTWT; wavelet transform; analysis; study; algorithm; details; computation of coefficients

RAJMIC, P.; PRŮŠA, Z.

2014

1. 1. 2014

World Scientific Publishing Company

0219-6913

International Journal of Wavelets Multiresolution and Information Processing

12

1

Republic of Singapore

1450001-1

1450001-38

38

http://www.worldscientific.com/doi/abs/10.1142/S0219691314500015