Wavelet questions?

Dear all,

I have three quesitons.

1. DWT subband coding uses both low-pass filter and high-pass filter.
Are these two filters QMF filters? Just two filters here, what is the
matter with Wavelet?

For QMF filter, only cos(a*w) can be perfect reconstruction and linear
phase. DWT is perfect reconstruction and FIR is with linear phase. Also
DWT should be QMF filters. They are not matching. I feel confused on
this point.

2. If I want to use wavelet multirate processing for TV signal, how do
I construct the low-pass filter and high-pass filter? What is the issue
here?

3. Lifting scheme is for fast DWT. Can any DWT transform use lifting
scheme?

I'll try and answer your questions, although I don't really go around
calling myself an expert, I study wavelets in my spare time, I just don't
like seeing unanswered messages :)

The filters DO have to conform to QMF parameters for reconstruction of the
original signal, I believe the high & low pass have to be symmetrical in
some way, I believe Mallet's book will provide details (its heavy on the
maths though)

http://www.amazon.co.uk/Wavelet-Signal-Processing-Analysis-Applications/dp/012466606X/sr=1-14/qid=1168260421/ref=sr_1_14/026-3427322-3216441?ie=UTF8&s=books

As I understand it, you can perform a DWT transform without QMF filters,
but the results will probably be very strange unless you intentional
wanted that ;)

If you are writing computer code to perform a DWT transform using your own
filters, I would test it first using some pre-existing filters, such as
those defined by Haar (the simplest of all) or Daubechies.  That way you
have a point of reference when you come to implementing some of the more
advanced stuff, such as the lifting scheme.

Generally, you don't need to define your own filters at all, but find a
pre-existing one that would suit your needs, from the texts I've read,
everybody seems to be using Gabor wavelets, regardless of application!
(not sure if this will suit your needs though, it comes in a slightly
different form, to that of a high and low pass filter)

I haven't worked on the lifting scheme of the DWT, but I am looking at
other methods for fast DWT's based on FFT computations, and some
pre-conditions have to be set in order for the fastest possible algorithm,
which is probably associated to the filters.

also, you could also try and post for help on www.wavelet.org, although
they only seem to answer questions that have never been asked before (and
as a result the forum appears dead), but they do have an archive you can
browse through.

- Moose.
>

>I have three quesitons.
>
>1. DWT subband coding uses both low-pass filter and high-pass filter.
>Are these two filters QMF filters? Just two filters here, what is the
>matter with Wavelet?

>
>For QMF filter, only cos(a*w) can be perfect reconstruction and linear
>phase. DWT is perfect reconstruction and FIR is with linear phase. Also
>DWT should be QMF filters. They are not matching. I feel confused on
>this point.
>
>2. If I want to use wavelet multirate processing for TV signal, how do
>I construct the low-pass filter and high-pass filter? What is the issue
>here?
>
>3. Lifting scheme is for fast DWT. Can any DWT transform use lifting
>scheme?
>
>

Thanks, moose.

One more question.

JPEG 2000 uses a different Wavelet from Gabor wavelet. What is the
motivation? What is the issue when we choose a wavelet? Any materials
about comparison on gabor, haar, and Daubechies.

Thanks,



moosedude wrote:
> I'll try and answer your questions, although I don't really go around
> calling myself an expert, I study wavelets in my spare time, I just don't
> like seeing unanswered messages :)
>
> The filters DO have to conform to QMF parameters for reconstruction of the
> original signal, I believe the high & low pass have to be symmetrical in
> some way, I believe Mallet's book will provide details (its heavy on the
> maths though)
>
> http://www.amazon.co.uk/Wavelet-Signal-Processing-Analysis-Applications/dp/012466606X/sr=1-14/qid=1168260421/ref=sr_1_14/026-3427322-3216441?ie=UTF8&s=books
>
> As I understand it, you can perform a DWT transform without QMF filters,
> but the results will probably be very strange unless you intentional
> wanted that ;)
>
> If you are writing computer code to perform a DWT transform using your own
> filters, I would test it first using some pre-existing filters, such as
> those defined by Haar (the simplest of all) or Daubechies.  That way you
> have a point of reference when you come to implementing some of the more
> advanced stuff, such as the lifting scheme.
>
> Generally, you don't need to define your own filters at all, but find a
> pre-existing one that would suit your needs, from the texts I've read,
> everybody seems to be using Gabor wavelets, regardless of application!
> (not sure if this will suit your needs though, it comes in a slightly
> different form, to that of a high and low pass filter)
>
> I haven't worked on the lifting scheme of the DWT, but I am looking at
> other methods for fast DWT's based on FFT computations, and some
> pre-conditions have to be set in order for the fastest possible algorithm,
> which is probably associated to the filters.
>
> also, you could also try and post for help on www.wavelet.org, although
> they only seem to answer questions that have never been asked before (and
> as a result the forum appears dead), but they do have an archive you can
> browse through.
>
> - Moose.
> >
>
> >I have three quesitons.
> >
> >1. DWT subband coding uses both low-pass filter and high-pass filter.
> >Are these two filters QMF filters? Just two filters here, what is the
> >matter with Wavelet?
>
> >
> >For QMF filter, only cos(a*w) can be perfect reconstruction and linear
> >phase. DWT is perfect reconstruction and FIR is with linear phase. Also
> >DWT should be QMF filters. They are not matching. I feel confused on
> >this point.
> >
> >2. If I want to use wavelet multirate processing for TV signal, how do
> >I construct the low-pass filter and high-pass filter? What is the issue
> >here?
> >
> >3. Lifting scheme is for fast DWT. Can any DWT transform use lifting
> >scheme?
> >
> >

Its difficult to find a comparison on types of wavelets, merely because its
difficult to quantify and is usually very specific to application, you are
probably going to have to do a little bit of research yourself, into the
different wavelets and find out what others have chosen when faced with
the same problem.  

Generally, its a compromise of some sort choosing which parts of the
original data is the most important, and which parts you want the most
detailed information from, your choose of wavelet will affect this.

However, Don't even bother looking at Haar wavelets, They are good if you
need a worked example to help you understand some of the theory &
mathematics associated with wavelets (a good starting point to learn from)
but for a reliable, good performing algorithm thats practical, look
elsewhere.  But don't misunderstand me, as I say, its a good starting
point when you have never faced wavelets before, lots of worked example
are easy to find using Haar wavelets and can be extended to work with
other types.

The daubechie, D2 (2 co-efficients) wavelet is essentially the same as a
Haar wavelet, but daubechie wavelets can be generated with a varying
number of different co-efficients, such as D4 (4 co-efficients) and above
..

Gabor wavelets are good for looking at data with patterns and structure
such as music.

Cannot really comment on the JPEG standard, haven't really spent much time
looking at that, But I have found a link on the web, which explains why the
FBI, when looking for a storage method for fingerprints, didn't choose the
JPEG standard...

http://www.c3.lanl.gov/~brislawn/FBI/FBI.html

Hopefully, I have helped a little!  Mostly I think you're going to
spending some time on google researching this!

and finally, http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html

- Moose.

>Thanks, moose.
>
>One more question.
>
>JPEG 2000 uses a different Wavelet from Gabor wavelet. What is the
>motivation? What is the issue when we choose a wavelet? Any materials
>about comparison on gabor, haar, and Daubechies.
>
>Thanks,
>
>
>
>moosedude wrote:
>> I'll try and answer your questions, although I don't really go around
>> calling myself an expert, I study wavelets in my spare time, I just
don't
>> like seeing unanswered messages :)
>>
>> The filters DO have to conform to QMF parameters for reconstruction of
the
>> original signal, I believe the high & low pass have to be symmetrical
in
>> some way, I believe Mallet's book will provide details (its heavy on
the
>> maths though)
>>
>>
http://www.amazon.co.uk/Wavelet-Signal-Processing-Analysis-Applications/dp/012466606X/sr=1-14/qid=1168260421/ref=sr_1_14/026-3427322-3216441?ie=UTF8&s=books
>>
>> As I understand it, you can perform a DWT transform without QMF
filters,
>> but the results will probably be very strange unless you intentional
>> wanted that ;)
>>
>> If you are writing computer code to perform a DWT transform using your
own
>> filters, I would test it first using some pre-existing filters, such
as
>> those defined by Haar (the simplest of all) or Daubechies.  That way
you
>> have a point of reference when you come to implementing some of the
more
>> advanced stuff, such as the lifting scheme.
>>
>> Generally, you don't need to define your own filters at all, but find
a
>> pre-existing one that would suit your needs, from the texts I've read,
>> everybody seems to be using Gabor wavelets, regardless of application!
>> (not sure if this will suit your needs though, it comes in a slightly
>> different form, to that of a high and low pass filter)
>>
>> I haven't worked on the lifting scheme of the DWT, but I am looking at
>> other methods for fast DWT's based on FFT computations, and some
>> pre-conditions have to be set in order for the fastest possible
algorithm,
>> which is probably associated to the filters.
>>
>> also, you could also try and post for help on www.wavelet.org,
although
>> they only seem to answer questions that have never been asked before
(and
>> as a result the forum appears dead), but they do have an archive you
can
>> browse through.
>>
>> - Moose.
>> >
>>
>> >I have three quesitons.
>> >
>> >1. DWT subband coding uses both low-pass filter and high-pass filter.
>> >Are these two filters QMF filters? Just two filters here, what is the
>> >matter with Wavelet?
>>
>> >
>> >For QMF filter, only cos(a*w) can be perfect reconstruction and
linear
>> >phase. DWT is perfect reconstruction and FIR is with linear phase.
Also
>> >DWT should be QMF filters. They are not matching. I feel confused on
>> >this point.
>> >
>> >2. If I want to use wavelet multirate processing for TV signal, how
do
>> >I construct the low-pass filter and high-pass filter? What is the
issue
>> >here?
>> >
>> >3. Lifting scheme is for fast DWT. Can any DWT transform use lifting
>> >scheme?
>> >
>> >
>
>