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From: Gert Baars on 16 Sep 2005 10:45
What is the identity (formula) of a Kaiser-Bessel window.
I need something like W[n] = F(n,alpha)= .........?


From: Clay S. Turner on 16 Sep 2005 12:19

"Gert Baars" <g.baars13(a)chello.nl> wrote in message
news:534da$432adaa6$3ea3a972$11938(a)news.chello.nl...
> What is the identity (formula) of a Kaiser-Bessel window.
> I need something like W[n] = F(n,alpha)= .........?
>
>

Gert,


w[n] = I0[ beta*(1-[ (n-alpha)/alpha]^2 )^0.5] / I0(beta)
0 <= n <=M and alpha = M/2

= 0 otherwise


I0() is the zeroth order modified Bessel function of the 1st kind

I hope this helps,

Clay






From: Gert Baars on 16 Sep 2005 19:04
Clay S. Turner wrote:
> "Gert Baars" <g.baars13(a)chello.nl> wrote in message
> news:534da$432adaa6$3ea3a972$11938(a)news.chello.nl...
>
>>What is the identity (formula) of a Kaiser-Bessel window.
>>I need something like W[n] = F(n,alpha)= .........?
>>
>>
>
>
> Gert,
>
>
> w[n] = I0[ beta*(1-[ (n-alpha)/alpha]^2 )^0.5] / I0(beta)
> 0 <= n <=M and alpha = M/2
>
> = 0 otherwise
>
>
> I0() is the zeroth order modified Bessel function of the 1st kind
>
> I hope this helps,
>
> Clay
>
>
>
>
>
>
Thank you, it does help. Alpha is a value I can specify in
ScopeFIR but beta and IO[x] are not. I assume beta is a fixed
value in ScopeFIR.
From: Clay S. Turner on 16 Sep 2005 20:05

"Gert Baars" <g.baars13(a)chello.nl> wrote in message
news:7864a$432b4f9a$3ea3a972$10530(a)news.chello.nl...
>>
> Thank you, it does help. Alpha is a value I can specify in
> ScopeFIR but beta and IO[x] are not. I assume beta is a fixed
> value in ScopeFIR.

Hello Gert,

Actually you should be able to specify both. As I wrote the formula, M is
the length of the window. Alpha is simply M/2. This just makes the formula
simpler to write. Beta is what you adjust to trade bandwidth with rolloff.

Clay




From: BobM on 16 Sep 2005 20:30
Gert Baars wrote:
> Clay S. Turner wrote:
> > w[n] = I0[ beta*(1-[ (n-alpha)/alpha]^2 )^0.5] / I0(beta)
> > 0 <= n <=M and alpha = M/2
> >
> > = 0 otherwise
> >
> >
> > I0() is the zeroth order modified Bessel function of the 1st kind
> >
> > I hope this helps,
> >
> > Clay
> >
> >
> >
> >
> >
> >
> Thank you, it does help. Alpha is a value I can specify in
> ScopeFIR but beta and IO[x] are not. I assume beta is a fixed
> value in ScopeFIR.

In that formula, Beta is the parameter that you define. Alpha is
already defined as M/2. So in ScopeFIR, Alpha is Beta.

You don't define I0 when creating the window. I0() is the zeroth order
modified Bessel function of the 1st kind. If you're trying to create
the window from scratch you'll need to be able to generate this. Check
here:

http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html

Regards,
Bob

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