k - spsc - Graz University of Technology
k - spsc - Graz University of Technology
k - spsc - Graz University of Technology
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SPSC – Signal Processing & Speech Communication Lab<br />
Comparing these results, we can conclude:<br />
ψ<br />
k n<br />
And in particular for k = 0 and n = 0:<br />
( ) (<br />
k<br />
t = h<br />
* a nT − t)<br />
*<br />
ψ ( t) = ( t) = h ( − t)<br />
for the orthonormal case fk<br />
( t) = h<br />
*<br />
k ( − t)<br />
00<br />
ψ<br />
k<br />
H<br />
Discrete – Time Wavelet Transform<br />
Starting with the frequency domain relation and a scaling factor a = 2<br />
k<br />
k<br />
j<br />
( e ) ( ) ω j2<br />
ω<br />
= H e K k is a nonnegative int eger<br />
H<br />
jω<br />
( e )<br />
for highpass and k = 1, k = 2<br />
figure 15: Magnitude responses<br />
Pr<strong>of</strong>essor Georg Holzmann, Horst Cerjak, Christian 19.12.2005 Wallinger 12.06.07 Wavelet T. - Relation to Filter Banks<br />
33
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