FFT windows

Does anybody know if the FTT window cos2n(t) have an official name. I call 
it the Moriat window because one of my frinds started a discussion abot this 
window.

Jens Hee
www.jenshee.dk 

Jens Hee wrote:
> Does anybody know if the FTT window cos2n(t) have an official name.

It's called the "Von Hann" window:
http://en.wikipedia.org/wiki/Window_function#Hann_window

> I call
> it the Moriat window because one of my frinds started a discussion abot this
> window.

This friend's name is Moriat? He must be pretty old to claim precedence
over Julius von Hann. Check out

http://en.wikipedia.org/wiki/Julius_von_Hann

Regards,
Andor
> 
> Jens Hee
> www.jenshee.dk

Yes,  but only for n= 1 (what I mean but cannot type is that the exponent of 
cos is 2n

Jens


"Andor" <andor.bariska@gmail.com> wrote in message 
news:1147287886.754334.51150@j73g2000cwa.googlegroups.com...
>
> Jens Hee wrote:
>> Does anybody know if the FTT window cos2n(t) have an official name.
>
> It's called the "Von Hann" window:
> http://en.wikipedia.org/wiki/Window_function#Hann_window
>
>> I call
>> it the Moriat window because one of my frinds started a discussion abot 
>> this
>> window.
>
> This friend's name is Moriat? He must be pretty old to claim precedence
> over Julius von Hann. Check out
>
> http://en.wikipedia.org/wiki/Julius_von_Hann
>
> Regards,
> Andor
>>
>> Jens Hee
>> www.jenshee.dk
> 

Jens Hee wrote:

> Yes,  but only for n= 1 (what I mean but cannot type is that the exponent of
> cos is 2n

Ok, a whole window family defined by

w_n(t) = (0.5 - 0.5 Cos(t) )^n,  0 <= t <= 2 Pi

As you said, for n=1 this is the von Hann window. For n=2 you have

w_2(t) =  0.375 - 0.5 Cos(t) + 0.125 Cos(2 t)

this is close, but not equal to the Blackman window. For n=3

w_3(t) = 0.3125 - 0.46875 Cos(t) + 0.1875 Cos(2 t) - 0.03125 Cos(3 t)

which is not close to any window with a name. This means it is not
optimal in any sense (same for n=2). Look at the window link in
wikipedia to see the optimal third order cosine windows. Another good
link:

A H Nuttall:
"Some Windows with Very Good Sidelobe Behavior"
IEEE Transactions on Acoustics, Speech, and Signal Processing. Vol.
ASSP-29 (February 1981). 

Regards,
Andor