Hi, I am trying to use Kaiser-Bessel window before FFT. However, I am a bit confused about what is the difference between Kaiser and Kaiser-Bessel window. There is a definition of Kaiser window: http://en.wikipedia.org/wiki/Kaiser_window and also definition of Kaiser-Bessel derived (KBD) window. According to this document, Kaiser and Kaiser-Bessel windows are the same: http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/windows/#kaiser Here the National Instruments has its own definition of Kaiser-Bessel window: http://zone.ni.com/reference/en-XX/help/371361D-01/lvanls/kaiser_bessel_window/ And here is one more definition of Kaiser-Bessel window: http://arc.id.au/FilterDesign.html Is the Kaiser-Bessel window the same as Kaiser, and the Bessel means only that for Kaiser window computation the Bessel function of the first kind is used? In the MATLAB, only the kaiser window is implemented by default, as I know. Thanks, Afi

# Kaiser window vs Kaiser-Bessel window

Started by ●February 1, 2010

Reply by ●February 1, 20102010-02-01

Afinko wrote:> Hi, > > I am trying to use Kaiser-Bessel window before FFT. > However, I am a bit confused about what is the difference between Kaiser > and Kaiser-Bessel window. > > There is a definition of Kaiser window: > http://en.wikipedia.org/wiki/Kaiser_window > and also definition of Kaiser-Bessel derived (KBD) window. > > According to this document, Kaiser and Kaiser-Bessel windows are the > same: > http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/windows/#kaiser > > Here the National Instruments has its own definition of Kaiser-Bessel > window: > http://zone.ni.com/reference/en-XX/help/371361D-01/lvanls/kaiser_bessel_window/ > > And here is one more definition of Kaiser-Bessel window: > http://arc.id.au/FilterDesign.html > > Is the Kaiser-Bessel window the same as Kaiser, and the Bessel means only > that for Kaiser window computation the Bessel function of the first kind is > used? > > In the MATLAB, only the kaiser window is implemented by default, as I > know.I'm a bit rusty on this, but IIRC, the terms "Kaiser window" and "Kaiser-Bessel" window are nearly synonymous. I believe this original Kaiser window was basically a Kaiser-Bessel window with some particular parameter. Therefore, for systems like ScopeDSP, ScopeFIR, and Matlab that provide a Kaiser-Bessel window, there isn't any real need for a "Kaiser" window: just use the appropriate parameter to get that if you really want it. For brevity, Matlab calls their Kaiser-Bessel window function "kaiser". However, in ScopeDSP and ScopeFIR, the term "Kaiser-Bessel" is used; no "Kaiser" window is provided. (As Parks-McClellan bufs can attest, the Matlab folks have been known to be rather sloppy with terminology. ;-) BTW, if you use 4.0 for the alpha parameter of the Kaiser-Bessel window, you get something that's very similar to the famous 4-point Blackman-Harris windows. The canonical definitions of data windows are given in the classic paper "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform", by Fredric J. Harris, Proceedings of the IEEE, Vol 66, No. 1, January 1978. I think that paper has been updated, though I don't have the reference handy for the update - I'm sure someone else here does. Grant -- _____________________________________________________________________ Grant R. Griffin Publisher of dspGuru http://www.dspguru.com Iowegian International Corporation http://www.iowegian.com See http://www.iowegian.com/img/contact.gif for e-mail address

Reply by ●February 1, 20102010-02-01

I found a matlab code for generating "Kaiser-Bessel derived (KBD) window": http://www.ee.columbia.edu/~marios/mdct/mdct_giraffe.html kbdwin.m With this function, such KBD windows can be generated: http://en.wikipedia.org/wiki/File:Kbd-window.jpg And, these are not like the Kaiser windows (generated by kaiser.m) at all: http://en.wikipedia.org/wiki/File:KaiserWindow.jpg Which means, that at least, "Kaiser" and "Kaiser-Bessel derived" windows are not the same.

Reply by ●February 1, 20102010-02-01

Afinko wrote:> I found a matlab code for generating "Kaiser-Bessel derived (KBD) window": > http://www.ee.columbia.edu/~marios/mdct/mdct_giraffe.html > kbdwin.m > > With this function, such KBD windows can be generated: > http://en.wikipedia.org/wiki/File:Kbd-window.jpg > > And, these are not like the Kaiser windows (generated by kaiser.m) at > all: > http://en.wikipedia.org/wiki/File:KaiserWindow.jpg > > Which means, that at least, "Kaiser" and "Kaiser-Bessel derived" windows > are not the same.Sorry about that. Can you tell us the advantage of the Kaiser window over the Kaiser-Bessel window? Grant -- _____________________________________________________________________ Grant R. Griffin Publisher of dspGuru http://www.dspguru.com Iowegian International Corporation http://www.iowegian.com See http://www.iowegian.com/img/contact.gif for e-mail address

Reply by ●February 1, 20102010-02-01

>Sorry about that. Can you tell us the advantage of the Kaiser window >over the Kaiser-Bessel window? > >GrantWell, I have no idea what is the difference between "Kaiser", "Kaiser-Bessel", or "Kaiser-Bessel derived" window. I am totally confused. But I found in few papers, that "Kaiser-Bessel derived" window is commonly used in Advanced Audio Coding (AAC) codec. Is there someone, who is clear in this topic? Thanks, Afi

Reply by ●February 1, 20102010-02-01

On 1 Feb, 12:41, "Afinko" <afi...@gmail.com> wrote:> Hi, > > I am trying to use Kaiser-Bessel window before FFT. > However, I am a bit confused about what is the difference between Kaiser > and Kaiser-Bessel window.Unless somebody comes up with very compelling arguments to do otherwise, I'd interpret 'Kaiser-Bessel' the same way as 'Dolph-Chebychev': Kaiser used Bessel functions to design his window just the same way Dolph used Chebychev polynomials to design his. Rune

Reply by ●February 1, 20102010-02-01

On 01/02/2010 13:36, Grant Griffin wrote:> Afinko wrote: >> I found a matlab code for generating "Kaiser-Bessel derived (KBD) >> window": >> http://www.ee.columbia.edu/~marios/mdct/mdct_giraffe.html >> kbdwin.m >> >> With this function, such KBD windows can be generated: >> http://en.wikipedia.org/wiki/File:Kbd-window.jpg >> >> And, these are not like the Kaiser windows (generated by kaiser.m) at >> all: >> http://en.wikipedia.org/wiki/File:KaiserWindow.jpg >> >> Which means, that at least, "Kaiser" and "Kaiser-Bessel derived" windows >> are not the same. > > Sorry about that. Can you tell us the advantage of the Kaiser window > over the Kaiser-Bessel window? >The picture referenced above shows some (relatively) strange-looking windows; one looks like a gothic arch, the others with increasing amounts of flat-topness. That is definitely different from a "classic" Kaiser window which with the right param can be made to closely approximate Hann, Gaussian, etc. Richard Dobson

Reply by ●February 1, 20102010-02-01

Afinko wrote:>>Sorry about that. Can you tell us the advantage of the Kaiser window >>over the Kaiser-Bessel window? >> >>Grant > > > Well, I have no idea what is the difference between "Kaiser", > "Kaiser-Bessel", or "Kaiser-Bessel derived" window. I am totally confused. > But I found in few papers, that "Kaiser-Bessel derived" window is commonly > used in Advanced Audio Coding (AAC) codec. > > Is there someone, who is clear in this topic?KBD window is Kaiser window modified in the way so overlapped DCT would be invertible. http://en.wikipedia.org/wiki/Modified_discrete_cosine_transform http://en.wikipedia.org/wiki/Kaiser_window#Kaiser-Bessel_derived_.28KBD.29_window Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com