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3. Create DWT

This allows to build a structure of type DWT. Enter a Name for your DWT structure or Get it from the Variables list, and give the name of the vector that contains the wavelet coefficients on the line wt. The Index is a vector that gives the position of the first element of each scale level in the DWT. Finally, the Length is a vector that contains the number of coefficients at each scale. Of course, this is just 2^j at scale j.

Let us take an example. Starting from the signal sig with 2^n points, compute its DWT, called dwt_sig. This structure contains three vectors, dwt_sig.wt, dwt_sig.index and dwt_sig.length. Note that the coefficients are stored scale by scale, starting from the finest one. Also, the first values in dwt_sig.wt are not the wavelet coefficients, but values giving, in this order, the length of the original signal, the number of octaves, and finally the values identifying the filter that defines the wavelet. The number of these values depends on the particular filter. Thus, for instance, with a Daubechies-2 wavelet, and a 6-octaves transform, you'll get that the first 6 values of dwt_sig.wt are 2^n, 6, 0, 1.0000, 0.7071, and 0.7071. The first value that does correspond to a wavelet coefficient of sig is the one with index dwt_fBm00.index(1), which, in this case, is 7. dwt_fBm00.index(2) will be equal to 2^(j-1) + dwt_fBm00.index(1), etc...

A possible use of sub-menu is to first compute the DWT of a given signal, and then to press the Get all button at the bottom of the sub-menu window. You can then edit individually each of the components of the DWT structure, and then create a new DWT by pressing Create. For instance, you could take dwt_sig.wt and put a threshold so that all "small" coefficients become zero (this is the principle of the wavelet denoising method).


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