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 />
STFT as a Bank <strong>of</strong> Filters<br />
Expansion <strong>of</strong> Definiton for further insight!<br />
X<br />
STFT<br />
(<br />
jω<br />
)<br />
− jωm<br />
∞ e , m = e ∑<br />
n=<br />
−∞<br />
x(<br />
n)<br />
v(<br />
n<br />
−<br />
m)<br />
e<br />
jω(<br />
m−n)<br />
with:<br />
v(<br />
n − m)<br />
e<br />
jω(<br />
m−n)<br />
=<br />
v(<br />
−(<br />
m − n))<br />
e<br />
jω(<br />
m−n)<br />
Convolution <strong>of</strong> x(n) with the impulse response <strong>of</strong> the LTI – System<br />
v(−n)<br />
e<br />
jωn<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 />
7
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