Quantitative analysis of EEG signals: Time-frequency methods and ...

k h(k) g(k) p 2 (k) q 2 (k)
-10 0.00157 -0.00388
-9 0.01909 -0.03416
-8 -0.00503 0.03416
-7 -0.0444 0.07933
-6 0.01165 -0.02096
-5 0.10328 -0.18408
-4 -0.02593 0.04977 0.00208
-3 -0.24373 0.42390 -0.06040
-2 0.03398 -0.14034 0.25 0.30625
-1 0.65523 -0.90044 0.75 -0.63125
0 0.65523 0.90044 0.75 0.63125
1 0.03398 0.14034 0.25 -0.30625
2 -0.24373 -0.42390 -0.06040
3 -0.02593 -0.04977 -0.00208
4 0.10328 0.18408
5 0.01165 0.02096
6 -0.0444 -0.07933
7 -0.00503 -0.00901
8 0.01909 0.03416
9 0.00157 0.00388
Table 1: Filter coecients for quadratic B-Splines. h and g are the decomposition lters
and p 2 , q 2 are the reconstruction ones (from Ademoglu et al, 1997 see also Strang and
Nguyen, 1996).
2. Time-frequency resolution: it was shown that B-Spline functions have nearly optimal
time-frequency resolution (i.e. nearly the maximum allowed by the uncertainty
principle Unser et al., 1992).
3. Compact support: this means that the wavelet function does not extend to innity.
This fact is important in order not to include in a certain wavelet coecient
correlations with points far in the past or in the future.
4. Semi-orthogonality: the use of B-Splines as mother functions when applying the
multiresolution decomposition guarantees orthogonalitybetween the dierent scales.
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