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 RE: Normalization of gabor atoms [ Reply ]By: Supratim Ray on 2008-07-21 13:59 [forum:98168] Dear Remi To reduce the problem of a sudden discontinuity in the atoms (which are non-zero for windowLen followed by NFFT-windowLen zeros), I made the windowLength equal to the FFTsize, and decreased the value of the window-opt parameter. But now there appears to be a different problem: the dictionary is no longer complete. In your implementation, the window is given by exp(-1/(2*opt*(N+1)^2)), where N is the window size. When compared to the standard form of exp(-pi/s^2), yields a scale of s such that s^2 = 2*pi*opt*(N+1)^2. Hence if opt is less than 1/(8*pi) ~0.04, s is less than N/2. The scale of a gaussian atom determines its spread (temporal spread of s and spectral spread of 1/s). It appears that for small opt values, the edge of the signal is not covered. Consider a window and FFT size of N=512, with a Windowshift = 64. With only these atoms, the decomposition is just like doing a STFT with a constant window. The problem is that the maximum center position of an atom in your implementation is only upto L - N/2, where L is the length of the signal, which leaves the last N/2 points "uncovered" if the scale is less than N/2. As an example, I tried to reconstruct a signal (that I sent in the previous email) with the following dictionary 0.2 The decomposition, not surprisingly, fails to pick out the atom centered at n=1000 completely. However, as you mentioned before, this is a problem only at the edges of the signal (not a big issue for very long signals I suppose). For short duration signals, however, this would lead to some problems. regards, Supratim