k - spsc - Graz University of Technology

SPSC – Signal Processing & Speech Communication Lab
Orthonormal Basis
{ ()}
Of particular interest is the case where ψ k
t is a set of orthonormal
n
functions
Therefore, we expect:
∞
∫ψ *
k
−∞
n
() t ψ () t dt = δ ( k − l) δ ( n − m)
l m
using Parseval’s theorem, this becomes
1
2π
∞
∫
−∞
Ψ
*
k n
( jΩ) Ψ ( jΩ) dΩ = δ ( k − l) δ ( n − m)
l m
and get :
X
DWT
∞
∫
−∞
*
( k, n) x() t ψ () t
= dt
k n
Professor Georg Holzmann, Horst Cerjak, Christian 19.12.2005 Wallinger 12.06.07 Wavelet T. - Relation to Filter Banks
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