A question about wavelets

[billano786]

Can any one explain how to filll the frequency time dyadic grid after calculating DWT?

As an example let us say the signal is (1,2,3,4) now I apply Haar wavelet transform to get wavelet coeff (time and scale). now how do i construct time-frequency tiling diagram??

 

[odesus]

Hi!! Are you talking about wavelet representations like these?

in fact for practical purposes they're the same.. I will explain you how to fill wavelet in dydadic grid graphics...

 

[billano786]

Yes i am talking of the grid drawn in blue.

 

[odesus]

Hi!! Sorry not answering soon.

Ok.. the first thing you should know about using this scale-time diagram, is principally the fact is for continuous wavelet transform. The common expression for CWT in function of frecuency is the substitucion of parameter scale (commonly named a or s) by this expresion:

a=f0/f where f is the frecuency of your signal and f0 is the central frecuency of wavelet mother. Then in a normalized way:

a=fof/fs where fs is the sampling frecuency.

ok, you talk about a x(t) signal with discrete values 1,2,3,4. Firstable for working with this dyadic grid you should take care of next comments:

1.- We need to know your sampling frecuency and your signal frecuency.

2.- Take in consideration the use of dyadic grid. The name dyadic comes of the scale you choose for working your wavelet. Because we work with digital sistems with only 2 discrete values (0,1) it's easy to work with it. The translation of wavelet mother commonly used is 1 or in wavelet terms b=1.

3.- Remember sampling changes in a factor of scale you choose on every level, that's way for j=6.. your scale is 2^6=32 sampling points and your next level would be 16, the nex one.. 8 and so on.

4.- Nyquist should be consider or not, well it depens on you.. for wavelet nyquist is not an issue. Nyquist is important for us if we want reconstruct the original signal. Remember this when choose your fs.

I strongly recommend to you use DWT, CWT is just a cheat of our computers they work with discrete values anyway.

Let me know if this was useful for you Regards.