help -- Windzilla (high dynamic range windows)

On 10/25/2010 10:08 AM, Steve Pope wrote:

>
> In my case I probably could use something very much like a Nuttall, but
> which decays even faster.
>

> Steve

Steve,

The rate of decay is related to the edges of the window.  In particular, 
if the edges are zero-valued, the decay is related to the *order* of the 
zeros of the window function at the edge of the window.
And, there are well-known window functions that exploit this or similar 
ideas.

I found this that looks pretty good and uses some of the same terminology:
http://archive.chipcenter.com/dsp/DSP000308F1.html

and this:
http://zone.ni.com/reference/en-XX/help/371361B-01/lvanlsconcepts/char_smoothing_windows/

Fred

On Oct 25, 10:08 am, spop...@speedymail.org (Steve Pope) wrote:
>... Selecting the length is the less tricky part: the
> resolution bandwith is proportional to 1 / (window length), and may
> even be equal to (1 / (window length)) mutliplied by a metric
> quoted by Dale in his presentatoin (the 3dB bandwith in "bins").
> (But I'm trying to better understand this and other metrics in
> Dale's work.)

The correct parameter for resolution bandwidth is the effective noise
bandwidth (ENBW). The -3dB bandwidth is close.

>  ,,,
> In my case I probably could use something very much like a Nuttall, but
> which decays even faster.
> ...

As we have discussed before, saying "Nuttall" for a window is
gibbrish, unless possibly, you are referring to the two parameter
family of Bessel windows he suggested as a multidimensional extension
of the van der Mass class of optimal windows. (OK, I didn't mention
Nuttall's two parameter Bessel family before.)

Nuttall clearly and correctly (but not simply) labeled the windows he
described in the 1981 ASSP Transactions paper. If you want people
understand your statement tell us which you mean from the 18 windows
in the table in his most frequency cited windows paper. Nuttall's
descriptions are descriptive and functional. References that don't
understand the windows well enough to name them correctly probably
don't understand the window choices. Look for better.

Nuttall's paper is available at
http://www.ingelec.uns.edu.ar/pds2803/Materiales/Articulos/0084nutt.pdf

The last page of my posting at the 2010 comp.dsp conference has an
assortment of windows papers and where they are available on the web.
If any succumb to web rot, let me know and I'll try to find new
sources.

In my writeup, the term bin is used to refer to the members of the set
of basis function correlations calculated in a dft. If you want to use
frequency units, the separation between adjacent bins is Fs/window
size. I default Fs to 1.0. The paper figures are not labeled with
frequency units because they are applicable to transforms of spacial
sampling as well as temporal sampling.

Dale B. Dalrymple

dbd  <dbd@ieee.org> wrote:

>On Oct 25, 10:08 am, spop...@speedymail.org (Steve Pope) wrote:

>>... Selecting the length is the less tricky part: the
>> resolution bandwith is proportional to 1 / (window length), and may
>> even be equal to (1 / (window length)) mutliplied by a metric
>> quoted by Dale in his presentatoin (the 3dB bandwith in "bins").
>> (But I'm trying to better understand this and other metrics in
>> Dale's work.)

>The correct parameter for resolution bandwidth is the effective noise
>bandwidth (ENBW). The -3dB bandwidth is close.

Thanks

>> In my case I probably could use something very much like a Nuttall, but
>> which decays even faster.

>As we have discussed before, saying "Nuttall" for a window is
>gibbrish, unless possibly, you are referring to the two parameter
>family of Bessel windows he suggested as a multidimensional extension
>of the van der Mass class of optimal windows. (OK, I didn't mention
>Nuttall's two parameter Bessel family before.)

Oops.  Yes, I now remember the objections to referring to the
most commonly used of Nuttall's window as "The Nuttall Window".
I'll avoid this in the future.

>In my writeup, the term bin is used to refer to the members of the set
>of basis function correlations calculated in a dft. If you want to use
>frequency units, the separation between adjacent bins is Fs/window
>size. 

Thanks, that was my assumption.

>I default Fs to 1.0. The paper figures are not labeled with
>frequency units because they are applicable to transforms of spacial
>sampling as well as temporal sampling.

My only objection, and it's a mild one, to the "bin" terminology 
is that these is nothing inherent about these window functions that 
leads one to using a discrete transform either when studying them or
when using one; in particular the definition and computaation of a PSD 
using a window does not involve using a discrete transform, even when 
the data being analyzed is discrete-time.

Specifically, the PSD of a continous time signal is defined at
all non-negative real frequencies, and the PSD of a discrete-time
signal is defined all frequencies in [0,pi).  "bins" suggests (to me)
the frequencies being considered are also discrete.  

Perhaps I am being nit-picky.

Steve

On Oct 26, 6:47�pm, spop...@speedymail.org (Steve Pope) wrote:
> ...
>
> Oops. �Yes, I now remember the objections to referring to the
> most commonly used of Nuttall's window as "The Nuttall Window".
> I'll avoid this in the future.
>
The most commonly used windows in Nuttall's survey are the ones
labeled: "Hanning", "Hamming" and "Blackman".
Which of these is it that you use? Which of it's parameters would you
like to improve and which are you willing to ease of on?

> >In my writeup, the term bin is used to refer to the members of the set
> >of basis function correlations calculated in a dft. If you want to use
>...

> My only objection, and it's a mild one, to the "bin" terminology
> is that these is nothing inherent about these window functions that
> leads one to using a discrete transform either when studying them or
> when using one; in particular the definition and computaation of a PSD
> using a window does not involve using a discrete transform, even when
> the data being analyzed is discrete-time.
>
> Specifically, the PSD of a continous time signal is defined at
> all non-negative real frequencies, and the PSD of a discrete-time
> signal is defined all frequencies in [0,pi). �"bins" suggests (to me)
> the frequencies being considered are also discrete. �
>
> Perhaps I am being nit-picky.

Perhaps you are confused.

> Steve

Outside of symbolic manipulation, how do -you- calculate a "PSD" of a
finite discrete sequence that is not equivalent to a calculation by a
discrete transform?

Dale B. Dalrymple

dbd  <dbd@ieee.org> wrote:

>On Oct 26, 6:47&#4294967295;pm, spop...@speedymail.org (Steve Pope) wrote:

>> My only objection, and it's a mild one, to the "bin" terminology
>> is that these is nothing inherent about these window functions that
>> leads one to using a discrete transform either when studying them or
>> when using one; in particular the definition and computaation of a PSD
>> using a window does not involve using a discrete transform, even when
>> the data being analyzed is discrete-time.

>Outside of symbolic manipulation, how do -you- calculate a "PSD" of a
>finite discrete sequence that is not equivalent to a calculation by a
>discrete transform?

You slipped the word "finite" in there, right before "discrete".

So leave out the "finite".   Do you then agree with me?

(This is not academic; very typically one computes the PSD of
rather long input series.)

Steve

dbd  <dbd@ieee.org> wrote:

>On Oct 26, 6:47&#4294967295;pm, spop...@speedymail.org (Steve Pope) wrote:

>> Oops. &#4294967295;Yes, I now remember the objections to referring to the
>> most commonly used of Nuttall's window as "The Nuttall Window".
>> I'll avoid this in the future.

>The most commonly used windows in Nuttall's survey are the ones
>labeled: "Hanning", "Hamming" and "Blackman".
>Which of these is it that you use? 

I have used the 4-term window in your "Hamming minimum sidelobe"
table, with coefficients:

0.3635819, -0.4891775, 0.1365995, -0.0106411

But I have also used the following similar window coefficients
which (at least sometimes) has given me slightly better results 
relative to my originally stated problem in this thread:

0.355768, -0.487396, 0.144232, -0.012604

Either has been called "Nuttall", in different places.

>Which of it's parameters would you
>like to improve and which are you willing to ease of on?

That is what I need to study further, relating my results to
the parameters of these windows.

Steve

On 10/26/2010 6:47 PM, Steve Pope wrote:

> My only objection, and it's a mild one, to the "bin" terminology
> is that these is nothing inherent about these window functions that
> leads one to using a discrete transform either when studying them or
> when using one; in particular the definition and computaation of a PSD
> using a window does not involve using a discrete transform, even when
> the data being analyzed is discrete-time.
>
...............

> Perhaps I am being nit-picky.
>
> Steve

Steve,

I don't think you're being nit-picky as there are a number of different 
spaces and Fourier transform pairs that can be considered very legitimately:

continuous / continuous  as in "Fourier Transform"
discrete / continuous  as in Fourier Series taken in the opposite 
direction but I didn't want to say "inverse Fourier Series"
continuous / discrete as in Fourier series.
discrete / discrete as in Discrete Fourier Transform.

Which expands to:

continuous / continuous  as in "Fourier Transform"
discrete / continuous periodic, infinite  as in opposite Fourier Series
continuous periodic, infinite / discrete as in Fourier Series.
discrete periodic infinite / discrete periodic infinite as in DFT.

And:

continuous, finite / continuous infinite as in Finite Fourier Transform.
continuous, infinite / continuous finite as in inverse Finite Fourier 
Transform
discrete (may be finite) / continuous periodic, infinite as in Discrete 
(maybe finite) Fourier Transform
continuous periodic, infinite / discrete (may be finite) As in Fourier 
Series
discrete periodic infinite / discrete periodic infinite as in Discrete 
Fourier Transform

well .... I hope I got those OK or close enough.

So, interestingly I guess, a finite discrete sequence considered 
initially may only be Fourier Transformed into a continous periodic, 
infinite function.  There is no other option in this context.
And your use seems to favor discrete / continous.

But, if we decide to *force* the Fourier Transform of a finite discrete 
sequence to be a Discrete Fourier Transform then we are also forcing the 
time sequence to be periodic, infinite instead of finite.

So, I think Dale's use of "bins" is fine as long as one understands we 
are talking about:
discrete / discrete

Both are fine .. if I didn't miss something.

Fred

On Oct 26, 7:36�pm, spop...@speedymail.org (Steve Pope) wrote:
> dbd &#4294967295;<d...@ieee.org> wrote:
> ...
> >Outside of symbolic manipulation, how do -you- calculate a "PSD" of a
> >finite discrete sequence that is not equivalent to a calculation by a
> >discrete transform?
>
> You slipped the word "finite" in there, right before "discrete".

The real world enforces the "finite" there. No one has sampled or
calculated an infinite data set.

>
> So leave out the "finite". &#4294967295; Do you then agree with me?
>

Without the "finite" it isn't DSP. You have claimed to describe a
calculation you actually intend to perform. That enforces the
"finite".

> (This is not academic; very typically one computes the PSD of
> rather long input series.)

If you can calculate over the size of the data set, it is finite even
if "rather long". It is a characteristic of the DFT of samples of
stochastic processes that N does not gracefully approach infinity.
Confusing the two is misleading.

>
> Steve

Dale B. Dalrymple

On Oct 26, 8:56�pm, spop...@speedymail.org (Steve Pope) wrote:
>...
>
> I have used the 4-term window in your "Hamming minimum sidelobe"
> table, with coefficients:
>
> 0.3635819, -0.4891775, 0.1365995, -0.0106411

In my "Minimum Sidelobe" table, Hamming is the 2 term entry. Hamming
is the 2 term cosine -sum minimum sidelobe window.

These coefficients are the 4 term cosine-sum minimum sidelobe window.
In a DSP context, "4 term minimum sidelobe window" would probably by
clear.

>
> But I have also used the following similar window coefficients
> which (at least sometimes) has given me slightly better results
> relative to my originally stated problem in this thread:
>
> 0.355768, -0.487396, 0.144232, -0.012604

These are the 4 term cosine-sum continuous 1st derivative window. It
sometimes appears abbreviated as "CS4C1D".

>
> Either has been called "Nuttall", in different places.

So you were aware of the ambiguity and chose to inflict it upon us?

> ...
> Steve

Dale B. Dalrymple

dbd <dbd@ieee.org> wrote:
> On Oct 26, 7:36&#4294967295;pm, spop...@speedymail.org (Steve Pope) wrote:
>> dbd &#4294967295;<d...@ieee.org> wrote:

>> >Outside of symbolic manipulation, how do -you- calculate a "PSD" of a
>> >finite discrete sequence that is not equivalent to a calculation by a
>> >discrete transform?

>> You slipped the word "finite" in there, right before "discrete".
 
> The real world enforces the "finite" there. No one has sampled or
> calculated an infinite data set.

Well, you can sample a periodic data set.  Most likely that still
counts as finite, but one should probably note the difference.
 
>> So leave out the "finite". &#4294967295; Do you then agree with me?
 
> Without the "finite" it isn't DSP. You have claimed to describe a
> calculation you actually intend to perform. That enforces the
> "finite".

-- glen