小波滤波器的问答

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Wavelet filters

Started by mariya ●August 15, 2005

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Hello

i am trying to implement a wavelet transform using digital filters! Could
anyone tell me how to design these filters. I have tried to use matlab
command FIR1 but it seems not to be a good way to design these filters!
Thank for your help

		
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Posted by Randy Yates ●August 15, 2005

"mariya" <[email protected]> writes:


          
 > Hello     >     > i am trying to implement a wavelet transform using digital filters! Could     > anyone tell me how to design these filters. I have tried to use matlab     > command FIR1 but it seems not to be a good way to design these filters!     > Thank for your help       
         
Hi,

My homework on wavelets from my DSP class at NCSU is on-line at 

  http://www.digitalsignallabs.com/hw8.zip

Open the zip file and read the file hw.pdf with Adobe Acrobat.
Specifically, read Appendix A, which gives an overview of 
Matlab's wavelet toolbox. I found I needed it for my own
sanity.

--Randy

-- 
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%%%% <[email protected]>           % 'Living' Thing', *A New World Record*, ELO
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Posted by Rune Allnor ●August 16, 2005

mariya skrev:

          
 > Hello     >     > i am trying to implement a wavelet transform using digital filters! Could     > anyone tell me how to design these filters. I have tried to use matlab     > command FIR1 but it seems not to be a good way to design these filters!       
         
The main difference between wavelets and other sub-band filters,
is that the wavelet filters are interrelated in a special way:

h_n(t) = 1/a_n * h'((t-b_n)/a_n)                             [1]

where h'(n) is the "mother wavelet". What [1] says, is that each
wavelet filter is generated by a sacled, translated and compressed
version of some basic wave (impulse response of the filter, as it
were). These "mother wavelets" can be quite simple (the "mexican
hat") or they can be veritable pains in the neck, like the Daubechie
wavelets.

The main point is that the wavelet transform introduces strong
requirements to the FIR filters. You will probably not be able
to use any FIR filter generator to design wavelet filters.

Rune

      

Posted by ●August 16, 2005

 > You will probably not be able     > to use any FIR filter generator to design wavelet filters.       
         
besides, you dont really need to as there are plenty of good wavelet
filters out there, many of which are included in the wavelet toolbox by
Matlab. Here are the ones listed in my version of Matlab...

    biorwavf    - Biorthogonal spline wavelet filters.
    cgauwavf    - Complex Gaussian wavelet.
    cmorwavf    - Complex Morlet wavelet.
    coifwavf    - Coiflet wavelet filter.
    dbaux       - Daubechies wavelet filter computation.
    dbwavf      - Daubechies wavelet filters.
    fbspwavf    - Complex Frequency B-Spline wavelet.
    gauswavf    - Gaussian wavelet.
    mexihat     - Mexican Hat wavelet.
    meyer       - Meyer wavelet.
    meyeraux    - Meyer wavelet auxiliary function.
    morlet      - Morlet wavelet.
    rbiowavf    - Reverse Biorthogonal spline wavelet filters.
    shanwavf    - Complex Shannon wavelet.
    symaux      - Symlet wavelet filter computation.
    symwavf     - Symlet wavelet filter.

      

Posted by mariya ●August 16, 2005

 >The main point is that the wavelet transform introduces strong     >requirements to the FIR filters. You will probably not be able     >to use any FIR filter generator to design wavelet filters.     >     >Rune     >     >       
         **********************************
Hi again,

If i understood correct you mean that i cannot get wavelet filters  using
FIR digital filters? I did handle some matlab wavelet filters but the
point is that i don't know what are their features such as cutoff or
sampling frequency. For instance to decompose the signal there are some
quit command such as
[C,L] = wavedec(X,N,'wname')
[C,L] = wavedec(X,N,Lo_D,Hi_D)
Here we need just to choose the wavelet name (let's say 'db3') suitable to
our application or the related filters (quit straight )! I would also use
the same filters for my wavelet transform on a processor but how to get
these filters coefficients??
thanx!
		
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Posted by Ikaro ●August 17, 2005

I am not sure which version you are using, but if you are using matlab
12.1 check:

http://www.mathworks.com/support/solutions/data/1-18NCG.html?solution=1-18NCG

      

Posted by Rune Allnor ●August 17, 2005

mariya skrev:

          
 > >The main point is that the wavelet transform introduces strong     > >requirements to the FIR filters. You will probably not be able     > >to use any FIR filter generator to design wavelet filters.     > >     > >Rune     > >     > >     > **********************************     > Hi again,     >     > If i understood correct you mean that i cannot get wavelet filters  using     > FIR digital filters?       
         
Yes you can, if the filter generator is set up to take into
account the particular aspects that wavelets depend on.

I am saying that you probably need specialized wavelet generators
to do that. The wavelets themselves are FIR filters.

Rune

      

Posted by mariya ●August 25, 2005

Hi,

Isn't it correct that the "dbaux command" gives the coefficients of the
wavelet reconstruction filters? Any suggestion on which command to use in
order to get the coefficients of the analysis filter. 
I am using matlab version 7.0!

Thanks for your time!
		
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Posted by mariya ●August 25, 2005

Hi,

Isn't it correct that the "dbaux command" gives the coefficients of the
wavelet reconstruction filters? Any suggestion on which command to use in
order to get the coefficients of the analysis filter. 
I am using matlab version 7.0!

Thanks for your time!
		
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小波工具里面最强大的莫过于Matlab的工具箱了。在Mathworks网站上也有类似的关于小波滤波器计算的问答

Subject: Computing wavelet filters

From: Najah

Date: 27 Sep, 2010 21:06:21

Message: 1 of 3

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Hi,

I am working on 2D wavelet Decomposition, and I want to extract the wavelet coefficients of the image on 3scales.

I have the code to extract the wavelet coefficients and I used the function

[LP,HP]=compute_wavelet_filter('Haar',8)

To compute the wavelet filters but when I applied these filters to the (wavefast)

function I got an error that LP and HP must be even and equal length real, numeric filter vectors.

Anyone can help ?

Thanks in advance.

Subject: Computing wavelet filters

From: Wayne King

Date: 27 Sep, 2010 21:53:06

Message: 2 of 3

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"Najah " <[email protected]> wrote in message <[email protected]>...

> Hi,

> I am working on 2D wavelet Decomposition, and I want to extract the wavelet coefficients of the image on 3scales.

> I have the code to extract the wavelet coefficients and I used the function

> [LP,HP]=compute_wavelet_filter('Haar',8)

> To compute the wavelet filters but when I applied these filters to the (wavefast)

> function I got an error that LP and HP must be even and equal length real, numeric filter vectors.

>

>

> Anyone can help ?

> Thanks in advance.

Hi Najah, I don't know the software you are using, but are you sure that

[LP,HP]=compute_wavelet_filter('Haar',8);

is returning anything meaningful? If you enter:

>>whos LP

>>whos HP

what is returned.

 If the second input argument to compute_wavelet_filter() iis the support size of the filter, the Haar wavelet only has one support size (2). So 'Haar',8 doesn't make any sense. If you were using a Daubechies wavelet, then you have many possible choices for the support (two times the number of vanishing moments).

What if you tried

[LP,HP]=compute_wavelet_filter('Daubechies',4);

Does your code work then?

Wayne

Subject: Computing wavelet filters

From: Najah

Date: 27 Sep, 2010 22:16:20

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"Wayne King" <[email protected]> wrote in message <[email protected]>...

> "Najah " <[email protected]> wrote in message <[email protected]>...

> > Hi,

> > I am working on 2D wavelet Decomposition, and I want to extract the wavelet coefficients of the image on 3scales.

> > I have the code to extract the wavelet coefficients and I used the function

> > [LP,HP]=compute_wavelet_filter('Haar',8)

> > To compute the wavelet filters but when I applied these filters to the (wavefast)

> > function I got an error that LP and HP must be even and equal length real, numeric filter vectors.

> >

> >

> > Anyone can help ?

> > Thanks in advance.

>

> Hi Najah, I don't know the software you are using, but are you sure that

>

> [LP,HP]=compute_wavelet_filter('Haar',8);

>

> is returning anything meaningful? If you enter:

>

> >>whos LP

> >>whos HP

>

> what is returned.

>

> If the second input argument to compute_wavelet_filter() iis the support size of the filter, the Haar wavelet only has one support size (2). So 'Haar',8 doesn't make any sense. If you were using a Daubechies wavelet, then you have many possible choices for the support (two times the number of vanishing moments).

>

> What if you tried

>

> [LP,HP]=compute_wavelet_filter('Daubechies',4);

>

> Does your code work then?

>

> Wayne

Thanks Wayne for your replay.

I tried it but it gives me the same error.

I used the code in this link

http://fourier.eng.hmc.edu/e161/dipum/wavefast.m

The code suggest another call to the wavefast by defining the wavelet name

"

[C, L] = WAVEFAST(X, N, WNAME) performs the same operation but

% fetches filters LP and HP for wavelet WNAME using WAVEFILTER.

"

I think I must tried it. but I dont know who can I wirte the WNAME?

最后的链接指向 冈萨雷斯的 数字图像处理（使用Matlab）的教材和附带的Matlab源码