k - spsc - Graz University of Technology

SPSC – Signal Processing & Speech Communication Lab
All synthesis filters are again generated from a fixed prototype synthesis filter
f(t) ( mother wavelet )
f
k
−k
2 −k
() t = a f ( a t)
Substituting this in the preceding equation and assuming perfect reconstruction, we get
with:
−k
() = ∑∑ ( ) ( − k
t X k,
n a f a t − nT )
2
x
DWT
k n
−k
k
k
−
2 −
−k
k
() t = f () t → ψ () t = a ψ ( a t − nT ) = a ψ [ a ( t − na T )] Kset
of basis functions
2
ψ
k n
using this, we can express each basis function in terms of the filter f k
( t)
ψ
k n
( ) (
k
t = f t − na T )
k
Professor Georg Holzmann, Horst Cerjak, Christian 19.12.2005 Wallinger 12.06.07 Wavelet T. - Relation to Filter Banks
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