DISCRETE WAVELET TRANSFORM OF FINITE SIGNALS: DETAILED STUDY OF THE ALGORITHM
Pavel Rajmic, Zdeněk Průša · International Journal of Wavelets Multiresolution and Information Processing · 2013
The paper presents a detailed analysis of algorithms used for the forward and the inverse discrete wavelet transform (DTWT) 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.