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 />
Another inversion formula is given by:<br />
2π<br />
∞<br />
1 ⎛<br />
∫ ∑ (<br />
jω<br />
)<br />
* ⎞<br />
= ⎜<br />
( − )<br />
jωn<br />
x( n)<br />
X<br />
STFT<br />
e , m v n m ⎟e<br />
dω<br />
2π<br />
⎝ m=−∞<br />
⎠<br />
0<br />
2<br />
∑ v = 1<br />
which is provided by ( m)<br />
m<br />
if<br />
∑<br />
m<br />
( m)<br />
2<br />
v ≠ 1<br />
but finite divide right side <strong>of</strong> the formula by<br />
∑ m<br />
v<br />
( m)<br />
2<br />
but if window energy is infinite one cannot apply this formulation<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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