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"?
Difference between Wavelet and Filter bank?
Started by ●January 31, 2007
Reply by ●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 ●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 ●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 ●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 ●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 ●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 ●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
