Downsampling after wavelet denoising

I am working on a time series which is sampled once every 10 minutes. I
found by inspection of the auto correlation function that the detail
coefficients indicates pure noise for more than 7 levels of wavelet (db10)
decomposition. So, I did 8 levels of wavelet decomposition and then set the
8 level detail coeff. to zero. I carried out the inverse transform, and now
I wonder how much I can downsample the series without loosing information?

Thanks

gkn wrote:
> I am working on a time series which is sampled once every 10 minutes. I
> found by inspection of the auto correlation function that the detail
> coefficients indicates pure noise for more than 7 levels of wavelet (db10)
> decomposition. So, I did 8 levels of wavelet decomposition and then set the
> 8 level detail coeff. to zero. I carried out the inverse transform, and now
> I wonder how much I can downsample the series without loosing information?
>

If I understand correctly, you've zeroed out the wavelet coefficients
for basis functions having the shortest support. These represent
(roughly) the frequency range from Pi/2 to Pi, so you could argue for
downsampling by a factor of two. But the thing about wavelets is that
the filters aren't perfect, so you're going to get some aliasing. To
see how much, looking at the frequency response of the scaling filter
for this particular wavelet.

David L. Rick
Hach Company

Header address is bot bait! Humans may use the following address:
davidDOTrickAThachDOTcomREMOVE