Window function

Hi,

I am looking for a window function that doesn't smear frequencies that fall
exactly into a frequency bin. I thougt the Hann window is a good choice,
but it still produces some smearing. Is there a better choice?

Regards,
Christian

(Thank you for calling it by its name, the Hann window.  There is hope for
humanity.  I happened to speak to Richard Hamming shortly before he died,
and he chuckled at the clueless unintentional honorific he sometimes
received via the Hann windowing function.)

Offhand, I thought Hann was exact, if numerically accurate.  This window's
frequency-domain rendition is, after all, FIR.

Max Hauser


"Christian" in  news:c59h0t$2oov6f$1@ID-177991.news.uni-berlin.de...
> Hi,
>
> I am looking for a window function that doesn't smear frequencies
> that fall exactly into a frequency bin. I thougt the Hann window is a
> good choice, but it still produces some smearing. Is there a better
> choice?

Christian wrote:
> 
> Hi,
> 
> I am looking for a window function that doesn't smear frequencies that fall
> exactly into a frequency bin. I thougt the Hann window is a good choice,
> but it still produces some smearing. Is there a better choice?

A rectangular window is the only window that will do that.


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Don't ask me to prove it, but windows, in effect, smear the smearing. In
exchange for reducing the smearing if off-center frequencies, they add
some to the centered ones. The best a good window can do is equalize
smearing and confine it to near-by bins. It's that no-free-lunch thing.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Max Hauser wrote:

> (Thank you for calling it by its name, the Hann window.  There is hope for
> humanity.  I happened to speak to Richard Hamming shortly before he died,
> and he chuckled at the clueless unintentional honorific he sometimes
> received via the Hann windowing function.)
> 
> Offhand, I thought Hann was exact, if numerically accurate.  This window's
> frequency-domain rendition is, after all, FIR.
> 
> Max Hauser
> 
> 
> "Christian" in  news:c59h0t$2oov6f$1@ID-177991.news.uni-berlin.de...
> 
>>Hi,
>>
>>I am looking for a window function that doesn't smear frequencies
>>that fall exactly into a frequency bin. I thougt the Hann window is a
>>good choice, but it still produces some smearing. Is there a better
>>choice?

Christian wrote:

> Hi,
> 
> I am looking for a window function that doesn't smear frequencies that fall
> exactly into a frequency bin. I thougt the Hann window is a good choice,
> but it still produces some smearing. Is there a better choice?
> 
> Regards,
> Christian

No such thing I'm afraid.  Think of it as a convolution in 
the frequency domain.  The only thing that could do what you 
want would be a rectangular window, i.e. none.


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

"Christian" <mca@nurfuerspam.de> wrote in message
news:c59h0t$2oov6f$1@ID-177991.news.uni-berlin.de...
> Hi,
>
> I am looking for a window function that doesn't smear frequencies that
fall
> exactly into a frequency bin. I thougt the Hann window is a good choice,
> but it still produces some smearing. Is there a better choice?
>
> Regards,
> Christian

Not exactly what you asked for ...
If you use a triangular window then every other sample in the spectrum won't
be smeared into, the smearing will decay very rapidly away from a sample of
large amplitude - at the expense of smearing between immediately adjacent
samples.

Fred

Maybe I misunderstood the question, but some windows have the special
property of finite, or controlled, spread with on-bin sinusoids, which is
not the same as smearing over the whole spectrum.  It has been an extremely
useful feature in some situations, and manifests itself as the window's
finitude in the frequency domain.  (Another consequence is that the
windowing can be computed efficiently in frequency domain if its support
there is short.)

"Bob Cain" in news:c59p8501aq9@enews4.newsguy.com...
> No such thing I'm afraid.  Think of it as a convolution in
> the frequency domain.  The only thing that could do what you
> want would be a rectangular window, i.e. none.

Thank you all for your answers!

I was afraid to hear exactly what you all told me ...
I recently used the so called "Schreier toolbox" which is a bunch of (very
useful) matlab scripts that deal with sigma delta converter design. In that
toolbox there is function which redefines the hann window (with an
asymmetric hann window), but the .m-file contains a comment that there is
no smearing of tones that fall exactly into a frequency bin.
Therefore I really got curious.

Regards,
Chris

Jerry Avins wrote:

> Don't ask me to prove it, but windows, in effect, smear the smearing. In
> exchange for reducing the smearing if off-center frequencies, they add
> some to the centered ones. The best a good window can do is equalize
> smearing and confine it to near-by bins. It's that no-free-lunch thing.
> 
> Jerry

Fred Marshall wrote:

> "Christian" <mca@nurfuerspam.de> wrote in message
> news:c59h0t$2oov6f$1@ID-177991.news.uni-berlin.de...
> 
>>Hi,
>>
>>I am looking for a window function that doesn't smear frequencies that
> 
> fall
> 
>>exactly into a frequency bin. I thougt the Hann window is a good choice,
>>but it still produces some smearing. Is there a better choice?
>>
>>Regards,
>>Christian
> 
> 
> Not exactly what you asked for ...
> If you use a triangular window then every other sample in the spectrum won't
> be smeared into, the smearing will decay very rapidly away from a sample of
> large amplitude - at the expense of smearing between immediately adjacent
> samples.
> 

Better rethink that, Fred.  Remember we are convolving the 
transform of a triangle with the frequency domain 
representation, not multiplying it.


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

"Bob Cain" <arcane@arcanemethods.com> wrote in message
news:c5amo3023jt@enews2.newsguy.com...
> Fred Marshall wrote:
>
> > "Christian" <mca@nurfuerspam.de> wrote in message
> > news:c59h0t$2oov6f$1@ID-177991.news.uni-berlin.de...
> >
> >>Hi,
> >>
> >>I am looking for a window function that doesn't smear frequencies that
> >
> > fall
> >
> >>exactly into a frequency bin. I thougt the Hann window is a good choice,
> >>but it still produces some smearing. Is there a better choice?
> >>
> >>Regards,
> >>Christian
> >
> >
> > Not exactly what you asked for ...
> > If you use a triangular window then every other sample in the spectrum
won't
> > be smeared into, the smearing will decay very rapidly away from a sample
of
> > large amplitude - at the expense of smearing between immediately
adjacent
> > samples.
> >
>
> Better rethink that, Fred.  Remember we are convolving the
> transform of a triangle with the frequency domain
> representation, not multiplying it.

Bob,

You're correct.  My error.

Fred