Wavelet filters

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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"mariya" <angelique1@jippii.fi> 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

-- 
%  Randy Yates                  % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC            %  sliding, it's magic."
%%% 919-577-9882                %  
%%%% <yates@ieee.org>           % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

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

> 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.

>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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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

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

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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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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