Thread Subject: Wavelet Transform - Upper-bound frequency instead of Nyquist frequency

Hello,

as to my knowledge, functions like 'wavedec' provided by the Wavelet Toolbox automatically take the Nyquist frequency as the maximum frequency when decomposing the frequency-time plane using low/band-pass filters.

Is there a simple way to pass those functions an alternative upper-bound frequency F < F_Nyquist to easily adapt the frequency range of the different sub-spaces without re-sampling the signal?

Thank you!

"Marc " <marc.weydert@student.kit.edu> wrote in message <j86gqu$9ne$1@newscl01ah.mathworks.com>...
> Hello,
>
> as to my knowledge, functions like 'wavedec' provided by the Wavelet Toolbox automatically take the Nyquist frequency as the maximum frequency when decomposing the frequency-time plane using low/band-pass filters.
>
> Is there a simple way to pass those functions an alternative upper-bound frequency F < F_Nyquist to easily adapt the frequency range of the different sub-spaces without re-sampling the signal?
>
> Thank you!

Hi Marc, the frequency content of your signal is determined before in gets into MATLAB. The wavelet transform has to work with what it's given.

Have you thought about wavelet packets? Wavelet packet analysis gives you an orthogonal transform with finer frequency splitting. If you don't care about having an orthogonal transform, you can use continuous wavelet analysis.

Wayne

> Hi Marc, the frequency content of your signal is determined before in gets into MATLAB. The wavelet transform has to work with what it's given.
>
> Have you thought about wavelet packets? Wavelet packet analysis gives you an orthogonal transform with finer frequency splitting. If you don't care about having an orthogonal transform, you can use continuous wavelet analysis.
>
> Wayne

Hi Wayne,
thanks for the quick reply!

Maybe I should give you an example to clarify what I mean.

Let's say I have a signal, sampled at 360Hz. No matter if I use continuous wavelet analysis or wavelet packet analysis, Matlab will take 180Hz as the upper-bound frequency. This will lead to a 5.625-11.25Hz range for the 5th level details.

Now let's say I would like to have another frequency range on that 5th level, e.g. 4-8Hz, which would match if Matlab takes 125Hz as upper-bound frequency.

So how can I adjust the frequency range of a given level without resampling?

Wavelet packets will only allow me to get finer sub-spaces for high frequencies?

"Marc " <marc.weydert@student.kit.edu> wrote in message <j86idj$fa1$1@newscl01ah.mathworks.com>...
> > Hi Marc, the frequency content of your signal is determined before in gets into MATLAB. The wavelet transform has to work with what it's given.
> >
> > Have you thought about wavelet packets? Wavelet packet analysis gives you an orthogonal transform with finer frequency splitting. If you don't care about having an orthogonal transform, you can use continuous wavelet analysis.
> >
> > Wayne
>
> Hi Wayne,
> thanks for the quick reply!
>
> Maybe I should give you an example to clarify what I mean.
>
> Let's say I have a signal, sampled at 360Hz. No matter if I use continuous wavelet analysis or wavelet packet analysis, Matlab will take 180Hz as the upper-bound frequency. This will lead to a 5.625-11.25Hz range for the 5th level details.
>
> Now let's say I would like to have another frequency range on that 5th level, e.g. 4-8Hz, which would match if Matlab takes 125Hz as upper-bound frequency.
>
> So how can I adjust the frequency range of a given level without resampling?
>
> Wavelet packets will only allow me to get finer sub-spaces for high frequencies?

The wavelet packet analysis yields many more details than the wavelet tree, but you're right one of them would be approximately: 5.625-11.25Hz

The intervals for the wavelet packet at level 5 with a sampling frequency of 360 Hz would be

n = 0:31;
lw = (360*n)/2^6;
up =(360*(n+1))/2^6;
intervals = [lw' up'];

You do not have that restriction with continuous wavelet analysis, you can refine your scale vector. You are not limited to dyadic scales, but you give up orthogonality. You can tailor your scales to your frequencies of interest with the CWT.

Wayne

Thanks a lot!