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SPSC – Signal Processing & Speech Communication Lab Choice of “Best Window” R oot M ean S quare duration of window function v(t) in time domain D t ∞ 2 1 2 2 D t ∫ t v E −∞ () t = dt frequency domain D f ∞ 2 1 2 2 D f ∫ Ω V ( jΩ) 2πE −∞ = dΩ with: 2 E . . . window energy E = v () t dt ∫ Uncertainty principle: D t D f ≥ 0.5 Iff Gaussian – window, this inequality becomes an equality ! Professor Georg Holzmann, Horst Cerjak, Christian 19.12.2005 Wallinger 12.06.07 Wavelet T. - Relation to Filter Banks 20
SPSC – Signal Processing & Speech Communication Lab Filter Bank Interpretation figure 10: continuous – STFT Professor Georg Holzmann, Horst Cerjak, Christian 19.12.2005 Wallinger 12.06.07 Wavelet T. - Relation to Filter Banks 21
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