Sorry about the many posts

>
>Cedron mentioned the Harris paper. It is the best of the early window
>review papers. In case you are not familiar with it, a proper citation
is:
>
>Harris, F.J. ”On the Use of Windows for Harmonic Analysis with the
>Discrete Fourier Transform.” Proceedings of the IEEE. Vol. 66, No.
>1
>(January 1978).
>

Thanks for the complete reference.  I think the reference in your "Windows
Connections" paper is better though:

harris, f.j., "On the Use of Windows for Harmonic Analysis with the
Discrete Fourier
Transform” Proc.IEEE, 66, pp. 51-83, January1978.

>
>For windows coefficients, plots of window performance and some other
>windows information, relationships and references see the presentation
paper:
>
>"Windows Connections"
>Dale B. Dalrymple 
>from the last comp.dsp Conference 
>http://www.abvolt.com/compdsp/presentations/Dalrymple/dbd.pdf
>
>I hope you have fun.
>
>Dale B. Dalrymple

In your paper you repeat the first misconception about interpreting the
discrete FT using concepts from the continuous FT that I mentioned in the
"New frequency estimator from two DFT bins" thread, namely, the falloff of
a complex tone in a DFT is the sinc function.  It is stated in the "This
is what you get with 'no window'." section under the "Middle plot" case. 
Jacobsen makes the same assertion earlier in this thread, but also
includes a parenthetical phrase with the correct answer, i.e. the
Dirichlet Kernel (seemingly implying they are the same).  The harris paper
gives the correct answer in Equation 7.  There is no reason for either you
or Jacobsen, or the numerous websites you can find it on, should continue
to make this misstatement as fact, you should know better.  Even those of
you who give zero weight to exactness.  Yes, the two functions are
similar, even good approximations of each other for larger N, but they are
not the same.

In general, like in Calculus, the continuous case is the limit value of
the discrete case.  Therefore, you can use the discrete case to make
inferences about the continuous case, but the reverse is much more
difficult, especially qualitatively.  In other words, given a sequence
that has a limit you can figure out what the limit is, but given just a
limit finding the sequence that gets you there is generally
indeterminable.

Earlier in this thread, I gave the equation for a window function which
corresponds to a convolution kernel I called the killer K:

[ cos( Pi/N ) - cos( Pi/N * (2n+1) ) ] * 1/2 = sin( Pi/N * (n+1) ) * sin(
Pi/N * n )

Since you clearly have the code for doing windows metrics, I would find it
very interesting, and I hope others would too, if you could plug it into
your code and report the results.

Ced
---------------------------------------
Posted through http://www.DSPRelated.com

On Wednesday, March 8, 2017 at 6:56:26 PM UTC-8, Cedron wrote:
> ...

The regular community at comp.dsp does pretty well at being supportive, where they have the knowledge, of anyone willing to learn and capable of expression and learning. We accept contributions from anyone. It's a news group! We are not so supportive or tolerant of those who troll comp.dsp with baseless claims in search of personal self-aggrandizement, who lack the technical skills, knowledge and intellectual honesty to justify their claims, who hold themselves to lesser standards than they claim to expect from others here. There is nothing in the tone and content of this post to indicate any other kind of behavior than this or to encourage me to change my mind about this and feed the troll.

Dale B. Dalrymple

>On Wednesday, March 8, 2017 at 6:56:26 PM UTC-8, Cedron wrote:
>> ...
>
>The regular community at comp.dsp does pretty well at being supportive,
>where they have the knowledge, of anyone willing to learn and capable of
>expression and learning. We accept contributions from anyone. It's a
news
>group! We are not so supportive or tolerant of those who troll comp.dsp
with
>baseless claims in search of personal self-aggrandizement, who lack the
>technical skills, knowledge and intellectual honesty to justify their
claims, who
>hold themselves to lesser standards than they claim to expect from
others
>here. There is nothing in the tone and content of this post to indicate
any
>other kind of behavior than this or to encourage me to change my mind
>about this and feed the troll.
>
>Dale B. Dalrymple

Dale,

How does perpetuating incorrect statements help anybody, particularly
those who are on the learning curve?

When I have pointed out the incorrect statement, provided the correct
statement, proved it with math (last spring), provided a reference from a
seminal paper in the field, and explained it conceptually, can you
possibly say what you just said?

Here it is again:  The sinc function is not the correct description for
side lobe drop off in a DFT.  Not for complex tones, and not for real
tones.

Rather than attack me, dispute the statement or accept it.  Saying "it's
close enough" is holding yourself to a lesser standard.  It's a
mathematical statement, so it is true or false.  It is not a matter of
opinion or consensus.

Pardon me if I disagree with your assessment that tolerance, support, and
willingness to learn are universal within this group.  I wish it were.  I
would have had a lot less trouble introducing the discoveries I have
made.

Ced
---------------------------------------
Posted through http://www.DSPRelated.com

>
>When I have pointed out the incorrect statement, provided the correct
>statement, proved it with math (last spring), 

Here is a little elaboration:

https://www.dsprelated.com/showthread/comp.dsp/340906-4.php#tabs1-chronological


On May 22, Jacobsen wrote:

"A rectangular window has a sinx/x transform in both continuous and
discrete forms"

The he continued with:

"Since the math is consistent from the fundamentals for the continuous or
discrete cases, it's a pretty basic characterstic of the FT."


On May 23, I call him out on it:

I provided the correct equations, numerical results, and this statement:

"Please note that:

limit[N --> Infinity] N*sin( Pi*x/N ) = Pi*x

Therefore the true equation approaches the normalized Sinc function as N
gets larger."

Then in a followup post I said:

"Based on the results I gave in the other reply it looks like you are
going to have to roll back some of what you just said.  You speak so
authoritatively that I almost believe you."

His reply to that was:

"You don't have to believe me.   What I wrote above is contained in many
texts on signal processing and Fourier Transforms.   Of course, you don't
have to believe them, either."

This is, of course, a variation of "If it's on the internet it must be
true."


On May 24, Jacobsen wrote:

"So, just to illustrate slightly better, I did the following today on
MathCAD while I was waiting on the phone or whatever:

http://ericjacobsen.org/dsp/dftsinc.pdf"

From that paper:

"May 23, 2016 ...

The sinc() is the FT of a rectangular function for the continuous case of
the FT, and the Dirichlet kernel is the FT of the rectangular function for
the discrete sampled case. As N, the number of samples in the transform,
goes to infinity or the sampling interval goes to zero, the Dirichlet
kernel converges to the sinc() function."

He completely changes his position to match mine sometime between May 23
and May 24.

He then goes on to give basically the same numerical treatment I had
already given in the thread.  Did he credit me for his new found
knowledge?  No, and he backdated his write up.  Did he ever admit that he
had it wrong? No.

You can go back and read the whole thread for yourself.  This is just one
case of the many headwinds I have encountered bringing my well founded
assertions to this group.  Tolerant and supportive?

Ced

---------------------------------------
Posted through http://www.DSPRelated.com

Cedron <103185@DSPRelated> wrote:

>Here it is again:  The sinc function is not the correct description for
>side lobe drop off in a DFT.  Not for complex tones, and not for real
>tones.

It's the correct description of the side lobe drop of for a rectangular
window.  

An N-point DFT preserves energy so if you're simply trying to measure
energy vs. frequency, a rectangular window followed by an N-point DFT
allows you to measure a sinc function at the output of the DFT
relative to input frequency, by taking the total energy.

For N small, as opposed to N approaching infinity, you do not as
much information that is interesting to a spectral analysis
of a chunk of input, but you still get a sinc curve when you sweep
the input with a single frequency.

Or am I smoking something here?

Steve

On Thu, 9 Mar 2017 18:59:39 +0000 (UTC), spope33@speedymail.org (Steve
Pope) wrote:

>Cedron <103185@DSPRelated> wrote:
>
>>Here it is again:  The sinc function is not the correct description for
>>side lobe drop off in a DFT.  Not for complex tones, and not for real
>>tones.
>
>It's the correct description of the side lobe drop of for a rectangular
>window.  
>
>An N-point DFT preserves energy so if you're simply trying to measure
>energy vs. frequency, a rectangular window followed by an N-point DFT
>allows you to measure a sinc function at the output of the DFT
>relative to input frequency, by taking the total energy.
>
>For N small, as opposed to N approaching infinity, you do not as
>much information that is interesting to a spectral analysis
>of a chunk of input, but you still get a sinc curve when you sweep
>the input with a single frequency.
>
>Or am I smoking something here?

You're not.

You and I and most people who have been doing dsp professionally for
very long use the terminology this way, i.e., sinc, sinx/x, whatever.
Hobbyist pedants with an axe to grind may wish to point out the subtle
difference with the Dirichlet kernel.    It's the same thing but
accounts for the circularity, so the difference is subtle.   As most
of us know who have actually practiced in this area for long, unless
the actual difference is important to the topic at hand, sinx/x or
sinc is the usual term used.





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On Wednesday, March 8, 2017 at 11:45:36 PM UTC-8, Cedron wrote:
> ...
> 
>. Pardon me if I disagree with your assessment that tolerance, support, and
>. willingness to learn are universal within this group.  I wish it were.  I
>. would have had a lot less trouble introducing the discoveries I have
>. made.
> 
> Ced

What I said was:"The regular community at comp.dsp does pretty well at being supportive, where they have the knowledge, of anyone willing to learn and capable of expression and learning."

I made no claim of tolerance or support for trolling attention seeking sock-puppets. Thank you for so quickly misrepresenting my post and proving my point about you.

Dale B. Dalrymple

<eric.jacobsen@ieee.org> wrote:

>On Thu, 9 Mar 2017 18:59:39 +0000 (UTC), spope33@speedymail.org (Steve

>>Cedron <103185@DSPRelated> wrote:

>>>Here it is again:  The sinc function is not the correct description for
>>>side lobe drop off in a DFT.  Not for complex tones, and not for real
>>>tones.

>>It's the correct description of the side lobe drop of for a rectangular
>>window.  

>>An N-point DFT preserves energy so if you're simply trying to measure
>>energy vs. frequency, a rectangular window followed by an N-point DFT
>>allows you to measure a sinc function at the output of the DFT
>>relative to input frequency, by taking the total energy.

>>For N small, as opposed to N approaching infinity, you do not have as
>>much information that is interesting to a spectral analysis
>>of a chunk of input, but you still get a sinc curve when you sweep
>>the input with a single frequency.

>>Or am I smoking something here?

>You're not.

>You and I and most people who have been doing dsp professionally for
>very long use the terminology this way, i.e., sinc, sinx/x, whatever.
>Hobbyist pedants with an axe to grind may wish to point out the subtle
>difference with the Dirichlet kernel.    It's the same thing but
>accounts for the circularity, so the difference is subtle.   As most
>of us know who have actually practiced in this area for long, unless
>the actual difference is important to the topic at hand, sinx/x or
>sinc is the usual term used.

Thanks.

I agree, and in the above I think the issue is that Cedric's phrase, 
"correct description for the side lobe drop off in a DFT" is not 
sufficiently defined.   It depends on what "the" means.  I described 
how to observe exactly a sinc curve in the DFT output (without any 
subtle differences).  

Now I'll have to look up what a Dirichlet kernel is ....


Steve

On Thursday, March 9, 2017 at 12:05:34 PM UTC-8, eric.j...@ieee.org wrote:
> ...
> 
> You and I and most people who have been doing dsp professionally for
> very long use the terminology this way, i.e., sinc, sinx/x, whatever.
> Hobbyist pedants with an axe to grind may wish to point out the subtle
> difference with the Dirichlet kernel.    It's the same thing but
> accounts for the circularity, so the difference is subtle.   As most
> of us know who have actually practiced in this area for long, unless
> the actual difference is important to the topic at hand, sinx/x or
> sinc is the usual term used.
> 

Before we continue to over-analyze this, I think it is time to treat the topic with the full seriousness it deserves. There are a number of 'sinc' functions. For example, there is the 'unnormalized sinc', there is the 'normalized sinc' and the 'periodic sinc'. There are posters here with a wide variety of feelings about the choices made by The Mathworks. I have used their Signal Processing Toolbox for many years. The documentation for their 'dirac' function is subtitled "Dirichlet or periodic sinc function". I think this represents a common and acceptable usage in casual talk. I think rb-j has zero base for his periodically repeated insistence on the use of the more technical "circular Dirichlet thingie" that can be found in a post referenced in this thread.

Dale B. Dalrymple

(Of course, all of us have abandoned any hope for the state of grace because we accept the use of notation that fails to make obvious the multi-dimensional extensions of the sinc function.)

On Thursday, March 9, 2017 at 5:43:23 PM UTC-5, dbd wrote:
>  
> 
> I think rb-j has zero base for his periodically repeated insistence on the use of the more technical "circular Dirichlet thingie" that can be found in a post referenced in this thread.
> 

so Dale, suppose we choose our unit time equal to the sampling period so that our sample rate and sampling period are equal to 1.  and let's say that x(t) is properly bandlimited, that its spectrum is zero for any frequencies (f, not omega) at or above 1/2 in magnitude.  i think maybe we need to restrict x(t) to be real.

now, suppose x(t) is periodic and we fortuitously have a period of N (the same as the size of the DFT).  since T=1, then

   x[n] = x(nT) = x(n)

   and x[n+N] = x[n]   for all integer n.

if we reconstruct the continuous-time x(t) from the discrete x[n] and we're willing to add up an infinite number of samples, i don't think anyone will disagree that:

   x(t) = \sum_{n=-\infty}^{\infty} x[n] sinc(t-n)

where sinc(u) = sin(pi u)/(pi u) .

you agree with that, right Dale?

the thing is that only N values of x[n] are unique and all of the x[n+mN] terms can be collected into a single term, right Dale?

   x(t) = \sum_{m=-\infty}^{\infty} \sum_{n=0}^{N} x[n+mN] sinc(t-n-mN)

        = \sum_{m=-\infty}^{\infty} \sum_{n=0}^{N} x[n] sinc(t-n-mN)

do you agree with that, Dale?  then do you agree with this:

   x(t) =  \sum_{n=0}^{N} x[n] \sum_{m=-\infty}^{\infty} sinc(t-n-mN)  ?

i hope you do.

so my question is, what do you think (substituting t-n = u) the latter summation resolves to be?

    g(u) = \sum_{m=-\infty}^{\infty} sinc(u - mN)


it's pretty clear that g(u+N) = g(u) for all u.  what do you think g(u), in a closed form, is?


r b-j