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 />
The Continuous - Time Case<br />
Main points:<br />
X<br />
STFT<br />
∞<br />
∫<br />
−∞<br />
− jΩ<br />
t<br />
( jΩ,τ<br />
) = x( t) v( t −τ<br />
) e dt ( STFT )<br />
x<br />
∞<br />
1<br />
2π<br />
∫<br />
j t<br />
()( t v t −τ<br />
) = X ( jΩ,<br />
τ ) e<br />
Ω dΩ<br />
( inv STFT )<br />
−∞<br />
STFT<br />
.<br />
x<br />
1 ∞ ∞<br />
*<br />
STFT<br />
.<br />
jΩ<br />
t<br />
() t = ⎜ X ( jΩ,<br />
τ ) v ( t −τ<br />
) dτ<br />
⎟e<br />
dΩ<br />
( inv STFT )<br />
2π<br />
∫⎜<br />
∫<br />
−∞<br />
⎛<br />
⎝<br />
−∞<br />
⎞<br />
⎟<br />
⎠<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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