Reply by Scott Seidman●February 12, 20072007-02-12
"Rune Allnor" <allnor@tele.ntnu.no> wrote in news:1171310840.091907.22020
@j27g2000cwj.googlegroups.com:
> The difference between filter anks and wavelets are, as you
> indicate, very small.
By its nature, wavelet analyis is multiresolution. This is unlike a filter
bank, where the concept of scale isn't very important. They are two
different beasts.
--
Scott
Reverse name to reply
Reply by Rune Allnor●February 12, 20072007-02-12
On 1 Feb, 00:00, "yijun_l...@yahoo.com" <yijun_l...@yahoo.com> wrote:
> Dear all,
>
> What is the difference between Wavelet and Filter bank? From my
> understanding, wavelet is a special case of filter bank. Is it
> correct?
>
> One thing I feel confused. Wavelet can be viewed as an impulse
> response of a filter. Some window functions also have the similiar
> response. Why bother to introduce a new concept "wavelet"?
As others have already indicated, lots of it has to do with
introducing new buzzwords.
The difference between filter anks and wavelets are, as you
indicate, very small. Some of the specific differences is that
wavelest usually are recursive in nature, and has constant Q
specifications. Are those properties very relevant? I don't know.
Those properties are, apparently, what the whole theory of
wavelets are based on.
Rune
Reply by Kostadin Dabov●February 2, 20072007-02-02
Hello there,
> What is the difference between Wavelet and Filter bank? From my
> understanding, wavelet is a special case of filter bank. Is it
> correct?
Wavelets are functions that along with a scaling function can form a
transform basis (or an overcomplete frame, for that matter) by
dilations and translations. "Wavelet" is also used to mean the
applications of such transformation (i.e. wavelet decomposition)
itself. In the multiresolution scheme, filterbanks are an efficient
tool to perform a wavelet decomposition. E.g., a dyadic wavelet
decomposition can be realized by a pair of iterated filterbanks
composed of a low- and a high-pass filters that are subject to
"perfect reconstruction" requirements (e.g., see quadrature mirror
filters).
Hence, in that sense, filterbanks are just one of the tools that can
be used to efficiently perform wavelet decompositions.
Regards,
Kostadin
> One thing I feel confused. Wavelet can be viewed as an impulse
> response of a filter. Some window functions also have the similiar
> response. Why bother to introduce a new concept "wavelet"?
Reply by dbd●February 1, 20072007-02-01
On Feb 1, 10:59 am, "Ikaro" <ikarosi...@hotmail.com> wrote:
> > One thing I feel confused. Wavelet can be viewed as an impulse
> > response of a filter. Some window functions also have the similiar
> > response. Why bother to introduce a new concept "wavelet"?
>
> Because implicit in the name "wavelet" is that this window has to
> fullfil the following properties:
>
> -specific in time
> -vanishing moments
> -admissibility condition (Fourier transform vanishes at the zero
> frequency, ie, bandpass spectrum)
>
> Not all windows fullfill these requirements, and the ones that do, can
> be called wavelelts.
>
The discrete fourier transform can be viewed as a set of convolutions
by a complex exponential. The real part of the complex exponential is
a cosine. The windowed real DFT can be viewed as a set of filters
where the filter coefficients are the cosine modulated versions of the
window. The wavelet tests should be applied to the cosine modulated
window coefficients, not the window itself. A wavelet transform might
be approached as a set of cosine modulated coefficient sets, but the
cosines would not be equally spaced in frequency and the coefficients
would be different for each modulating cosine.
Dale B. Dalrymple
http://dbdimages.com
Reply by Ikaro●February 1, 20072007-02-01
> One thing I feel confused. Wavelet can be viewed as an impulse
> response of a filter. Some window functions also have the similiar
> response. Why bother to introduce a new concept "wavelet"?
Because implicit in the name "wavelet" is that this window has to
fullfil the following properties:
-specific in time
-vanishing moments
-admissibility condition (Fourier transform vanishes at the zero
frequency, ie, bandpass spectrum)
Not all windows fullfill these requirements, and the ones that do, can
be called wavelelts.
I might be missing some other additional requiments, but these are the
most important ones that I can remember...
In addition, perfoming windowing, and wavelet analysis are two
different things (in wavelet you are actualy cross-correlating the
signal with a sliding and scaled family of windows, rather than simply
multiplying the whole signal with a single window .)
Reply by Vladimir Vassilevsky●February 1, 20072007-02-01
yijun_lily@yahoo.com wrote:
> Dear all,
>
> What is the difference between Wavelet and Filter bank? From my
> understanding, wavelet is a special case of filter bank. Is it
> correct?
Yes, you can treat it in that way if you like.
> One thing I feel confused. Wavelet can be viewed as an impulse
> response of a filter. Some window functions also have the similiar
> response. Why bother to introduce a new concept "wavelet"?
Because fools like cool buzzwords.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Reply by dbd●February 1, 20072007-02-01
On Jan 31, 3:00 pm, "yijun_l...@yahoo.com" <yijun_l...@yahoo.com>
wrote:
> Dear all,
>
> What is the difference between Wavelet and Filter bank?
...
> Why bother to introduce a new concept "wavelet"?
It is difficult to compete for funding with the originators of the
established terminology on 'their' terms. The sale works better if the
academics contribute an often practically irrelevant rigor to a new
terminology. If the funding lasts long enough you might discover that
what works well under the new terminology resembles what worked well
under the old terminology. But you can't make the change in
terminology without arguing some plausible differentiation (not in the
mathemetical sense of the term) from the old ways.
Dale B Dalrymple
http://dbdimages.com
Reply by yiju...@yahoo.com●January 31, 20072007-01-31
Dear all,
What is the difference between Wavelet and Filter bank? From my
understanding, wavelet is a special case of filter bank. Is it
correct?
One thing I feel confused. Wavelet can be viewed as an impulse
response of a filter. Some window functions also have the similiar
response. Why bother to introduce a new concept "wavelet"?