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 />
For perfect reconstruction x ˆ( n) = x( n)<br />
we can express<br />
X<br />
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )<br />
2<br />
4<br />
2<br />
2<br />
z = F z Y z + F z Y z + + F z Y z F z Y z<br />
0 0<br />
1 1<br />
...<br />
M −1<br />
M − 2 M −2<br />
+<br />
M −1<br />
M −1<br />
M −1<br />
and in time domain:<br />
x<br />
M −2<br />
∞<br />
∞<br />
2k<br />
+ 1<br />
M −1<br />
( n) = y ( m) f ( n − 2 m) + y ( m) f ( n − 2 m)<br />
∑∑<br />
∑<br />
k k<br />
k=<br />
0 m=−∞<br />
m=−∞<br />
M −1<br />
M −1<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 />
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