Kaiser window vs Kaiser-Bessel window

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

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

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.

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

>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?

Thanks,
Afi

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

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

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