Reference for Flattop window derivation

Hello,

I'm hoping someone could point me to a reference (paper, book, etc)
where the flattop window is derived. I can find the equation itself
without too much trouble, but I'd like to know where the equation
comes from.

I've tried the classic papers by Harris, and Nuttal but they didn't
discuss it. It seems like most people are interested in narrowing the
mainlobe and having low sidelobes, instead of a flat amplitude
response.

Thanks for your help.

Cheers,
David

On 2004-08-04 05:41:09 +0200, dspguy2@netscape.net (Dave Kirkland) said:

> Hello,
> 
> I'm hoping someone could point me to a reference (paper, book, etc)
> where the flattop window is derived. I can find the equation itself
> without too much trouble, but I'd like to know where the equation
> comes from.
> 
> I've tried the classic papers by Harris, and Nuttal but they didn't
> discuss it. It seems like most people are interested in narrowing the
> mainlobe and having low sidelobes, instead of a flat amplitude
> response.
> 
> Thanks for your help.
> 
> Cheers,
> David


Did you check the "usual" references?

Oppenheim, Willsky, Young, "Signals and Systems".
Proakis, Manolakis, "Introduction to Digital Signal Processing"
Oppenheim, Schafer, "Discrete-Time Signal Processing".

I believe you should find a discussion of this window type in one (or 
all) of them. I don't have access to my library so I can't check this 
for you from where I am now.
-- 
Stephan M. Bernsee
http://www.dspdimension.com

Matlab has this function, and their help file gives this reference:

[1] Gade, Svend and Herlufsen, H., "Use of Weighting Functions in DFT/FFT
Analysis (Part I)," Br�el & Kj�r, Windows to FFT Analysis (Part I) Technical
Review, No. 3, 1987, pp. 19-21.

"Dave Kirkland" <dspguy2@netscape.net> wrote in message
news:f609a830.0408031941.33128981@posting.google.com...
> Hello,
>
> I'm hoping someone could point me to a reference (paper, book, etc)
> where the flattop window is derived. I can find the equation itself
> without too much trouble, but I'd like to know where the equation
> comes from.
>
> I've tried the classic papers by Harris, and Nuttal but they didn't
> discuss it. It seems like most people are interested in narrowing the
> mainlobe and having low sidelobes, instead of a flat amplitude
> response.
>
> Thanks for your help.
>
> Cheers,
> David

"Barry Brown" <brown0_news2@nospam_agilent.com> wrote in message
news:1091635738.535425@cswreg.cos.agilent.com...
> Matlab has this function, and their help file gives this reference:
>
> [1] Gade, Svend and Herlufsen, H., "Use of Weighting Functions in DFT/FFT
> Analysis (Part I)," Br&#4294967295;el & Kj&#4294967295;r, Windows to FFT Analysis (Part I)
Technical
> Review, No. 3, 1987, pp. 19-21.

And the electronic link is
http://www.bksv.com/pdf/Bv0031.pdf
(courtesies to our friend Google)

Cheers
Bhaskar


>
> "Dave Kirkland" <dspguy2@netscape.net> wrote in message
> news:f609a830.0408031941.33128981@posting.google.com...
> > Hello,
> >
> > I'm hoping someone could point me to a reference (paper, book, etc)
> > where the flattop window is derived. I can find the equation itself
> > without too much trouble, but I'd like to know where the equation
> > comes from.
> >
> > I've tried the classic papers by Harris, and Nuttal but they didn't
> > discuss it. It seems like most people are interested in narrowing the
> > mainlobe and having low sidelobes, instead of a flat amplitude
> > response.
> >
> > Thanks for your help.
> >
> > Cheers,
> > David
>
>

Hi Guys, thanks for your replys. I have tried the regular references
that I have access to.

I did also find the B&K manual online. Unofrtunately it just has the
formula for the window and there isn't any reference for a derivation.

Thanks for you help though. I do appreciate it.

Cheers,
David

"Bhaskar Thiagarajan" <bhaskart@my-deja.com> wrote in message news:<2ncpr3Fvkc8sU1@uni-berlin.de>...
> "Barry Brown" <brown0_news2@nospam_agilent.com> wrote in message
> news:1091635738.535425@cswreg.cos.agilent.com...
> > Matlab has this function, and their help file gives this reference:
> >
> > [1] Gade, Svend and Herlufsen, H., "Use of Weighting Functions in DFT/FFT
> > Analysis (Part I)," Br&#4294967295;el & Kj&#4294967295;r, Windows to FFT Analysis (Part I)
>  Technical
> > Review, No. 3, 1987, pp. 19-21.
> 
> And the electronic link is
> http://www.bksv.com/pdf/Bv0031.pdf
> (courtesies to our friend Google)
> 
> Cheers
> Bhaskar
> 
> 
> >
> > "Dave Kirkland" <dspguy2@netscape.net> wrote in message
> > news:f609a830.0408031941.33128981@posting.google.com...
> > > Hello,
> > >
> > > I'm hoping someone could point me to a reference (paper, book, etc)
> > > where the flattop window is derived. I can find the equation itself
> > > without too much trouble, but I'd like to know where the equation
> > > comes from.
> > >
> > > I've tried the classic papers by Harris, and Nuttal but they didn't
> > > discuss it. It seems like most people are interested in narrowing the
> > > mainlobe and having low sidelobes, instead of a flat amplitude
> > > response.
> > >
> > > Thanks for your help.
> > >
> > > Cheers,
> > > David
> >
> >

"Dave Kirkland" <dspguy2@netscape.net> wrote in message
news:f609a830.0408091023.24d4c120@posting.google.com...
> Hi Guys, thanks for your replys. I have tried the regular references
> that I have access to.
>
> I did also find the B&K manual online. Unofrtunately it just has the
> formula for the window and there isn't any reference for a derivation.

I' m not sure I understand your quest for a 'derivation'. My understanding
of most of the windows used today are that they are 'found' by people
experimenting with a bunch of coefficients and studying the results.
You (or I) could take one of the known windows, modify some of their
coefficients (in their equation) and create a new window with new
properties - if the results are good, I might try to convince others to use
(perhaps even try to get my name on it). I'm sure you could just invent a
whole new equation out of the blue and it might have behavior that is
desirable in certain applications. Perhaps what you are looking for is the
class of equations that the flat top originated from?
I've heard of a guy who used to work at HP who 'compiled' a set of windows
for use in their Fourier Analyzers (I think his name was Potter). He took
the same root equation (not sure if it belonged to the cos^alpha(X) family
of windows) and played with the coefficient terms to generate his list of
windows (of course he ended up generating the classic Hann, Hamming, etc as
well). His catalog was considered a very precious possesion by the HPers of
those days (perhaps it still is precious?)

Flat Top windows seem to be of use mostly to people who care about amplitude
accuracy. I'm sure you can create a whole family of flat tops depending on
the answer to 'how accurate'.

Cheers
Bhaskar


> Thanks for you help though. I do appreciate it.
>
> Cheers,
> David
>
> "Bhaskar Thiagarajan" <bhaskart@my-deja.com> wrote in message
news:<2ncpr3Fvkc8sU1@uni-berlin.de>...
> > "Barry Brown" <brown0_news2@nospam_agilent.com> wrote in message
> > news:1091635738.535425@cswreg.cos.agilent.com...
> > > Matlab has this function, and their help file gives this reference:
> > >
> > > [1] Gade, Svend and Herlufsen, H., "Use of Weighting Functions in
DFT/FFT
> > > Analysis (Part I)," Br&#4294967295;el & Kj&#4294967295;r, Windows to FFT Analysis (Part I)
> >  Technical
> > > Review, No. 3, 1987, pp. 19-21.
> >
> > And the electronic link is
> > http://www.bksv.com/pdf/Bv0031.pdf
> > (courtesies to our friend Google)
> >
> > Cheers
> > Bhaskar
> >
> >
> > >
> > > "Dave Kirkland" <dspguy2@netscape.net> wrote in message
> > > news:f609a830.0408031941.33128981@posting.google.com...
> > > > Hello,
> > > >
> > > > I'm hoping someone could point me to a reference (paper, book, etc)
> > > > where the flattop window is derived. I can find the equation itself
> > > > without too much trouble, but I'd like to know where the equation
> > > > comes from.
> > > >
> > > > I've tried the classic papers by Harris, and Nuttal but they didn't
> > > > discuss it. It seems like most people are interested in narrowing
the
> > > > mainlobe and having low sidelobes, instead of a flat amplitude
> > > > response.
> > > >
> > > > Thanks for your help.
> > > >
> > > > Cheers,
> > > > David
> > >
> > >

On 3 Aug 2004 20:41:09 -0700, dspguy2@netscape.net (Dave Kirkland)
wrote:

>Hello,
>
>I'm hoping someone could point me to a reference (paper, book, etc)
>where the flattop window is derived. I can find the equation itself
>without too much trouble, but I'd like to know where the equation
>comes from.
>
>I've tried the classic papers by Harris, and Nuttal but they didn't
>discuss it. It seems like most people are interested in narrowing the
>mainlobe and having low sidelobes, instead of a flat amplitude
>response.
>
>Thanks for your help.
>
>Cheers,
>David

Hi,
  have ya' seen the following?

http://www.mathworks.com/access/helpdesk/help/toolbox/signal/tukeywin.html

I wonder if that's the "flattop" window you're 
referring to.

[-Rick-]

On 2004-08-11 15:45:26 +0200, r.lyons@_BOGUS_ieee.org (Rick Lyons) said:

> Hi,
>   have ya' seen the following?
> 
> http://www.mathworks.com/access/helpdesk/help/toolbox/signal/tukeywin.html
> 
> I wonder if that's the "flattop" window you're referring to.
> 
> [-Rick-]

No I don't think that's the one he was referring to. The FlatTop window 
has some negative coefficients as I recall...
-- 
Stephan M. Bernsee
http://www.dspdimension.com

Stephan M. Bernsee <spam@dspdimension.com> wrote in message news:<2nuoe0F4novtU1@uni-berlin.de>...
> On 2004-08-11 15:45:26 +0200, r.lyons@_BOGUS_ieee.org (Rick Lyons) said:
> 
> > Hi,
> >   have ya' seen the following?
> > 
> > http://www.mathworks.com/access/helpdesk/help/toolbox/signal/tukeywin.html
> > 
> > I wonder if that's the "flattop" window you're referring to.
> > 
> > [-Rick-]
> 
> No I don't think that's the one he was referring to. The FlatTop window 
> has some negative coefficients as I recall...

Hi Guys,

The flattop window I'm refering to is now available in Matlab's Signal
Processing Toolbox, via the "flattop" function.

As to why I'm interested in the derivation. I've seen a few versions
of flattop windows formulas. Some have 3 cosine terms, some have 4 and
some have 5. I've also seen different values for these coefficients.
So given that, I prefer to have the capability to derive my own, so
that the meet my own needs. I would assume that they have some
optimally flat response over a bin width, but I'd like to know the
specifics of how to create my own.

The paper by Harris shows how some of the most common windows are
derived, and in what sense they can be considered optimal.

Yes, I'm concerned with proper accuracy in measuring amplitude values.
That's why I'm interested in the Flattop window.

Thanks for any help.

Cheers,
David

"Bhaskar Thiagarajan" <bhaskart@my-deja.com> wrote in message
news:2nq0hcF32j21U1@uni-berlin.de...
> I've heard of a guy who used to work at HP who 'compiled' a set of windows
> for use in their Fourier Analyzers (I think his name was Potter). He took
> the same root equation (not sure if it belonged to the cos^alpha(X) family
> of windows) and played with the coefficient terms to generate his list of
> windows (of course he ended up generating the classic Hann, Hamming, etc
as
> well). His catalog was considered a very precious possesion by the HPers
of
> those days (perhaps it still is precious?)

Ah yes, Ron Potter's window papers.  Good stuff.  I could show them to you,
but then I'd have to kill you...

He made a collection of sum-of-cosine windows (not cos^alpha), where
sum-of-cosine means that the time-domain representation of the window is the
sum of a small number of cosine terms.  This was an important criteria in
the days when calculating all those cosines was time consuming...  Ron
Potter's work is still considered proprietary here at Agilent, although in
reality everything really useful has since been duplicated outside of
HP/Agilent.  For flat-top windows, I think he really did use manual
experimentation and tweaking until he had coefficients that met his needs.

-- 
Eric Backus
R&D Design Engineer
Agilent Technologies, Inc.
425-356-6010 Tel