Advertisement
Published in:
2011 | OriginalPaper | Chapter
Wavelet Transforms and Filter Banks
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Let
$$B=\{R_{2{k{\varphi}}}\}\begin{array}{ll}{M-1}\\{K=0}\end{array}\cup\{R_{2{k{\psi}}}\}\begin{array}{ll}{M-1}\\{K=0}\end{array} $$
be a time-frequency localized basis for
$$L^2(\mathbb{Z}_{N})$$
, where
$$\varphi$$
is the mother wavelet and
$$\psi $$
is the father wavelet. For every signal z in L
2
(
$$\mathbb{Z}_N$$
), we get, by the fact that B is an orthonormal basis for L
2
(
$$\mathbb{Z}_N$$
) and (8.3)
10.1
$$z = \sum\limits^{M-1}_{k=0} (z, R_{2k}\varphi)R_{2k}\varphi + \sum\limits^{M-1}_{k=0} (z, R_{2k}\psi)R_{2k}\psi.$$