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dyadic grid and wavelets

Started by Unknown March 8, 2006
In the following link
http://perso.wanadoo.fr/polyvalens/clemens/wavelets/wavelets.html#section4
there is a dyadic grid. Can you explain me what this grid shows?

thank you

leonadavinci@gmail.com wrote:
> In the following link > http://perso.wanadoo.fr/polyvalens/clemens/wavelets/wavelets.html#section4 > there is a dyadic grid. Can you explain me what this grid shows? > > thank you
The dots show where a wavelet would be "centered" for a given translation and scale. Only the points shown are valid translation/scale pairs. Cheers! --M
>In the following link >http://perso.wanadoo.fr/polyvalens/clemens/wavelets/wavelets.html#section4 >there is a dyadic grid. Can you explain me what this grid shows? > >thank you
Hi there, You are taking samples for frequency response analysis as 2.(i.e) S0=2 and hence the representation of these samples as dyadic grid. It's also possible that you can take S0=3, 4,... But usually it is suggested value is 2. From the fig.1 its clear that for the lowest scale you take more samples. (i.e) for higher frequency more samples of time and hence the resolution of time is higher for higher frequencies. As you proceed further with increase in Scale(decrease in freq.) lesser no. of samples of time shows that time resolution is decreased and hence you get more resolution in frequency. One can also say that as you calculate further, you take lesser no. of samples resulting in simpler calculation and hence its also like a fast computational algorithm. -San