wavelet question

Hi

I have just started reading about wavelets and I found
the online tutorial by Polikar very helpfull for understanding
the basics of the theory:
http://users.rowan.edu/~polikar/WAVELETS/WTpreface.html

But there are some issues that I struggle with and I thought
maybe you good people of comp.dsp can help me with.

In part III of the above tutorial:
(http://users.rowan.edu/~polikar/WAVELETS/WTpart3.html)

figure 3.7 is the CWT of a chirp signal with frequencies
30,20,10,5 Hz in this order.
I don't seem to be ale to interpret the CWT result. In particular
how do you interpret the value of CWT at largest translation.
What I can see from the plot is that we have all the scales
say at translation value 90 ? But this is not true seeing the
original signal (fig. 3.6) ! I should have better frequency resolution
at lower frequencies according to the theory.

Appreciate your help

H.

Henrietta Denoue wrote:
> Hi
>
> I have just started reading about wavelets and I found
> the online tutorial by Polikar very helpfull for understanding
> the basics of the theory:
> http://users.rowan.edu/~polikar/WAVELETS/WTpreface.html
>
> But there are some issues that I struggle with and I thought
> maybe you good people of comp.dsp can help me with.
>
> In part III of the above tutorial:
> (http://users.rowan.edu/~polikar/WAVELETS/WTpart3.html)
>
> figure 3.7 is the CWT of a chirp signal with frequencies
> 30,20,10,5 Hz in this order.
> I don't seem to be ale to interpret the CWT result. In particular
> how do you interpret the value of CWT at largest translation.
> What I can see from the plot is that we have all the scales
> say at translation value 90 ? But this is not true seeing the
> original signal (fig. 3.6) ! I should have better frequency resolution
> at lower frequencies according to the theory.

As far as I can tell, it is a matter of the time-bandwidth product.
You have to be aware that there is a limit to what frequency (or
scale) resolution can be achieved given an observation time.
The relation is roughly

   df >= 1/T                                               [1]

where df is the frequency resolution/accuracy and T is the
duration of the observation. Wavelets are sligtly different
from other filters in that they meet equation [1] by equality,
whereas other analyses might perform worse.

Rune