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From: FAISAL PEER MOAHMED on 10 May 2010 15:38
Hi

In dyadic decomposition using wavelets , Filter coefficients are kept constant. If one ignore the downsampling , it looks like same filters connected in series. Could any one help please .

Regards

Faisal
From: Wayne King on 10 May 2010 19:49
"FAISAL PEER MOAHMED" <pfaisalbe(a)gmail.com> wrote in message <hs9nau$jmc$1(a)fred.mathworks.com>...
> Hi
>
> In dyadic decomposition using wavelets , Filter coefficients are kept constant. If one ignore the downsampling , it looks like same filters connected in series. Could any one help please .
>
> Regards
>
> Faisal

Hi Faisal, I'm not sure what the question here is. Yes, you can think of it as a cascade of filters. And yes, the scaling and wavelet filter coefficients are kept the same and the filter is applied to the downsampled output.

Wayne
From: FAISAL PEER MOAHMED on 11 May 2010 07:44
Thanks Wayne

What I mean was , if you ignore down-sampling , it should look like same filters ( I mean filters having same filter coefficients ) are connected in series. In practical could I say that this has no meaning.

Down sampling keeps only even indexed samples. What changes takes place after down sampling regarding frequency aspect ?

In SWT there is no down sampling. Change is filter coefficients are updated with zero padding. Will it be same as the one in dwt (convolving input signal with same filter coefficients followed by down sampling) ?

Please help








"Wayne King" <wmkingty(a)gmail.com> wrote in message <hsa620$gt3$1(a)fred.mathworks.com>...
> "FAISAL PEER MOAHMED" <pfaisalbe(a)gmail.com> wrote in message <hs9nau$jmc$1(a)fred.mathworks.com>...
> > Hi
> >
> > In dyadic decomposition using wavelets , Filter coefficients are kept constant. If one ignore the downsampling , it looks like same filters connected in series. Could any one help please .
> >
> > Regards
> >
> > Faisal
>
> Hi Faisal, I'm not sure what the question here is. Yes, you can think of it as a cascade of filters. And yes, the scaling and wavelet filter coefficients are kept the same and the filter is applied to the downsampled output.
>
> Wayne
From: Wayne King on 11 May 2010 08:17
"FAISAL PEER MOAHMED" <pfaisalbe(a)gmail.com> wrote in message <hsbfu6$hnv$1(a)fred.mathworks.com>...
> Thanks Wayne
>
> What I mean was , if you ignore down-sampling , it should look like same filters ( I mean filters having same filter coefficients ) are connected in series. In practical could I say that this has no meaning.
>
> Down sampling keeps only even indexed samples. What changes takes place after down sampling regarding frequency aspect ?
>
> In SWT there is no down sampling. Change is filter coefficients are updated with zero padding. Will it be same as the one in dwt (convolving input signal with same filter coefficients followed by down sampling) ?
>
> Please help
>
>
>
>
>
>
>
>
> "Wayne King" <wmkingty(a)gmail.com> wrote in message <hsa620$gt3$1(a)fred.mathworks.com>...
> > "FAISAL PEER MOAHMED" <pfaisalbe(a)gmail.com> wrote in message <hs9nau$jmc$1(a)fred.mathworks.com>...
> > > Hi
> > >
> > > In dyadic decomposition using wavelets , Filter coefficients are kept constant. If one ignore the downsampling , it looks like same filters connected in series. Could any one help please .
> > >
> > > Regards
> > >
> > > Faisal
> >
> > Hi Faisal, I'm not sure what the question here is. Yes, you can think of it as a cascade of filters. And yes, the scaling and wavelet filter coefficients are kept the same and the filter is applied to the downsampled output.
> >
> > Wayne

Hi Faisal, downsampling can keep either the even coefficients, or the odd ones. There are two different "phases". Both would result in decimated wavelet transforms.

Suppose G(z) is your filter (in the z-domain) and X(z) is your input (again in the z-domain), then filtering the signal with g(n) is
G(z)X(x)

Now if you downsample the convolution of g(n) and x(n), that is (for the even phase):

1/2[(G(z^{1/2})X(z^{1/2})+G(-z^{1/2})X(-z^{1/2})]

you've stretched G(z)X(z) by a factor of two, added a shifted version of it to itself, and scaled the result by 1/2.

Read some of the theory of multirate signal processing. You will find detailed explanations of what happens.

Wayne
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