Reply by dbd June 10, 20152015-06-10
On Tuesday, June 9, 2015 at 5:54:56 AM UTC-7, Cedron wrote:
...
On Tuesday, June 9, 2015 at 1:33:31 AM UTC-7, dbd wrote:
> >Window DFT-even symmetry is desirable for phase linearity and the > >independence of real and imaginary components of each bin. > > > > Yes, misspoke a little. The window I presented is symmetric around > (N-1)/2.
But your choice of R is inconsistent with that symmetry as is the time direction scaling of the function, but, enough attention to irrelevant misdirection.
> Coincidentally (or not) that is the center point that Martin > Vicanek's DFT is rotated about to gain his solutions for his two bin > formula (see the "Show me some more numbers" thread for a link to his > paper).
Coincidentally and irrelevantly.
> Since there is a slight "twist" to the DFT of a real signal as in > reaches its flattened ends at the DC and Nyquist bins, the linearity and > separability might not actually be desirable goals.
Now this is stronger cruft than your suggestions on cooking test noise in another thread. But, I am impressed that you can "say that with a straight face". You have the abilities and inclinations to have a powerful future on the net.
> > Thanks for your reply. > > If you haven't read my blog article on the formula's derivation, there is > a section titled "Implicit Windowing" where I explain that the formula > effectively has a Von Hann like window factored in and how that dampens > the effects of other tones. > > Ced
I -have- read your blog article and I think that the section on Implicit Windowing is the most powerful part. Except, perhaps when a reader considers the application of "implicit". It is true that there are windows that can be described with 3 parameters and that your formula has a vector of length 3, so there is an implicit sharing of the number 3. Some might seek a stronger tie than that, but fortunately that isn't relevant to the true strength of the section. And about the windowing, your formula does not apply the supposed window coefficients as a convolution to the points used in the algorithm so a windowing is never performed. But that's OK because the fact that your algorithm works for a 10 point DFT, a size too small to satisfy your (incorrect) claim to "approximate" a "window" as N => infinity shows that the accuracy of your algorithm has nothing to do with your algorithm resembling windowing, so you are safe there. But back to the good news, I've always been interested in windows and I don't think there is any better choice of irrelevant jargon to get search engine hits for your blog than "implicit windows". The rest of your blog is yet another piece of the gobbledegook that hides behind the signal processing that actually gets implemented in the world and just won't draw the attention "implicit windows" will. Good choice! Dale B. Dalrymple
Reply by Cedron June 9, 20152015-06-09
[...snip...]
> >You came to comp.dsp asking for references to read. People must have
assumed
>that that implied that you were capable of benefiting from references.
Maybe
>that's not true. >
Close, but not correct. I came to share my discovery of a better formula. After searching the literature and not finding it, after emailing many professors and being sent on many haystack searches, I am asking if anyone is aware of my formulas existing anywhere in the literature, not references on the general topic. How can I validate that it is actually a new discovery not a rediscovery?
>Window DFT-even symmetry is desirable for phase linearity and the >independence of real and imaginary components of each bin. >
Yes, misspoke a little. The window I presented is symmetric around (N-1)/2. Coincidentally (or not) that is the center point that Martin Vicanek's DFT is rotated about to gain his solutions for his two bin formula (see the "Show me some more numbers" thread for a link to his paper). Since there is a slight "twist" to the DFT of a real signal as in reaches its flattened ends at the DC and Nyquist bins, the linearity and separability might not actually be desirable goals.
>Dale B. Dalrymple
Thanks for your reply. If you haven't read my blog article on the formula's derivation, there is a section titled "Implicit Windowing" where I explain that the formula effectively has a Von Hann like window factored in and how that dampens the effects of other tones. Ced --------------------------------------- Posted through http://www.DSPRelated.com
Reply by dbd June 9, 20152015-06-09
On Saturday, June 6, 2015 at 7:59:35 PM UTC-7, Cedron wrote:
...

> Everybody wants to send me to references to read, hunting in haystacks, so > to speak. In your own words, please tell me why windows should be > symmetric. At least you said "harris" and not "Harris". > > Ced
You came to comp.dsp asking for references to read. People must have assumed that that implied that you were capable of benefiting from references. Maybe that's not true. Window DFT-even symmetry is desirable for phase linearity and the independence of real and imaginary components of each bin. Dale B. Dalrymple
Reply by Cedron June 6, 20152015-06-06
>On Monday, June 1, 2015 at 12:53:34 PM UTC-7, Cedron wrote: > >... >> >> Here is a candidate window function: >> >> w_n = 2 [ cos( Pi/N ) - cos( (n+1/2) 2Pi/N ) ] >> >> = 4 sin( (n+1) Pi/N ) sin( n Pi/N ) >> >> Ced > >Since we keep suggesting the use of windows with DFTs, we ought to help
you
>with your understanding of the consequences of the 'digital' in DFT.
Your
>window lacks the proper symmetry for a digital window.
Here is the vector from my formula definition: r = e^( -i 2Pi/N ) W = ( -1, 1 + r, -r ) Since the numerator and denominator are linear in W, W can be arbitrarily rescaled and the formula will still work. Let s = e^( i Pi/N ) Ws = ( -s, -s + 1/s, -1/s ) Ws ~=~ ( -1, 2 -1 ) The window function I provided in the time domain corresponds to Ws applied in the frequency domain. You keep assuming I don't understand windows and what they do. So if you want to carry a window function through to the bin value formulas and then solve a frequency equation from there, this window function has the possibility of working well. I'll repeat myself, for frequency determination of a signal that is steady across the frame, I have not found any advantage in using a window function. Either in the real signal case or the complex signal case. Since my real signal frequency formula is clearly the best in the real signal case according to Julien's Figure 4, and it is as good as any of the DFT methods for the complex signal case in Figure 3, I would think the burden would be on you to provide a window function and a corresponding estimator to beat my unwindowed one.
> >Hint: the digital samples should be symmetric about the N/2 sample for a
N
>point DFT, that is, if you have a continuous symmetric window of length
N,
>zero only at the ends, only the first sample in the digital version of
the
>window will be zero. > >search comp.dsp for "DFT symmetric" >or google: harris proceedings windows > >Dale B. Dalrymple
Everybody wants to send me to references to read, hunting in haystacks, so to speak. In your own words, please tell me why windows should be symmetric. At least you said "harris" and not "Harris". Ced --------------------------------------- Posted through http://www.DSPRelated.com
Reply by dbd June 6, 20152015-06-06
On Monday, June 1, 2015 at 12:53:34 PM UTC-7, Cedron wrote:

...
> > Here is a candidate window function: > > w_n = 2 [ cos( Pi/N ) - cos( (n+1/2) 2Pi/N ) ] > > = 4 sin( (n+1) Pi/N ) sin( n Pi/N ) > > Ced
Since we keep suggesting the use of windows with DFTs, we ought to help you with your understanding of the consequences of the 'digital' in DFT. Your window lacks the proper symmetry for a digital window. Hint: the digital samples should be symmetric about the N/2 sample for a N point DFT, that is, if you have a continuous symmetric window of length N, zero only at the ends, only the first sample in the digital version of the window will be zero. search comp.dsp for "DFT symmetric" or google: harris proceedings windows Dale B. Dalrymple
Reply by Rick Lyons June 5, 20152015-06-05
On Wed, 3 Jun 2015 21:51:29 +0000 (UTC), spope33@speedymail.org (Steve
Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: > >>On Wed, 3 Jun 2015 12:14:42 -0700 (PDT), dbd > >>>There is a much smaller literature providing window designs for interferenc= >>>e suppression for testing done by the people who design 24 bit convertors t= >>>o evaluate their device internal implementations. Those are the minimum sid= >>>elobe windows in "Windows Connections" (pages 6 and 12) at: >>>http://www.abvolt.com/compdsp/presentations/Dalrymple/dbd.pdf > >>Ah, nostalgia. I remember when you presented that. Very cool. > >Was that in Kansas City? I had formed a plan to attend but in the >end did not. > >I have, however, used dbd's windows subsequently. They are very >good for measuring tiny spurs in the stopband of a much stronger >comm signal, therefore, useful for evaluating regulatory compliance. > >Steve
Hi Steve, Yep, that was the paper Dale presented in Kansa City in 2010. That conference was both educational and a good time. Vladimir Vassilevsky, and his lovely wife, put in much effort to make the conference a success. [-Rick-]
Reply by Steve Pope June 3, 20152015-06-03
Eric Jacobsen <eric.jacobsen@ieee.org> wrote:

>On Wed, 3 Jun 2015 12:14:42 -0700 (PDT), dbd
>>There is a much smaller literature providing window designs for interferenc= >>e suppression for testing done by the people who design 24 bit convertors t= >>o evaluate their device internal implementations. Those are the minimum sid= >>elobe windows in "Windows Connections" (pages 6 and 12) at: >>http://www.abvolt.com/compdsp/presentations/Dalrymple/dbd.pdf
>Ah, nostalgia. I remember when you presented that. Very cool.
Was that in Kansas City? I had formed a plan to attend but in the end did not. I have, however, used dbd's windows subsequently. They are very good for measuring tiny spurs in the stopband of a much stronger comm signal, therefore, useful for evaluating regulatory compliance. Steve
Reply by dbd June 3, 20152015-06-03
On Wednesday, June 3, 2015 at 9:54:31 AM UTC-7, robert bristow-johnson wrote:
> ... > in a 2001 paper (the only one i ever did for an IEEE thingie) i derived > an estimator for (middle) frequency, sweep rate, and ramp rate of a > gaussian-windowed chirp (assuming linearly swept frequency and > exponentially ramped amplitude within the narrow gaussian window) with a > collection (more than three) of adjacent points. > ... > r b-j rbj@audioimagination.com
There is a more general development of the process that has appeared under the term "frequency reassessment" at: http://perso.ens-lyon.fr/patrick.flandrin/0065-Ch05.pdf Time-frequency reassignment: from principles to algorithms Flandrin, Auger, Chassandre-Mottin and http://arxiv.org/abs/0903.3080 A Unified Theory of Time-Frequency Reassignment Kelly R. Fritz, Sean A. Fulop Dale B. Dalrymple
Reply by Eric Jacobsen June 3, 20152015-06-03
On Wed, 3 Jun 2015 12:14:42 -0700 (PDT), dbd
<d.dalrymple@sbcglobal.net> wrote:

>On Wednesday, June 3, 2015 at 3:20:00 AM UTC-7, tsd82 wrote: > >> ... >> By the way, I was wondering, does anyone knows about applications >> requiring to work at these very high SNR (60 - 100 dB) ? I have no idea >> for myself. Maybe very precise frequency measurements for atomic-based >> clock? >>=20 >> Kind Regards, >>=20 >> Julien > >There is a considerable literature on frequency peak location and measureme= >nt for the application of ADC and DAC testing. Think 24 bit convertors.
That would do it.
>There is a much smaller literature providing window designs for interferenc= >e suppression for testing done by the people who design 24 bit convertors t= >o evaluate their device internal implementations. Those are the minimum sid= >elobe windows in "Windows Connections" (pages 6 and 12) at: >http://www.abvolt.com/compdsp/presentations/Dalrymple/dbd.pdf > >Dale B. Dalrymple
Ah, nostalgia. I remember when you presented that. Very cool. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by dbd June 3, 20152015-06-03
On Wednesday, June 3, 2015 at 3:20:00 AM UTC-7, tsd82 wrote:

> ... > By the way, I was wondering, does anyone knows about applications > requiring to work at these very high SNR (60 - 100 dB) ? I have no idea > for myself. Maybe very precise frequency measurements for atomic-based > clock? > > Kind Regards, > > Julien
There is a considerable literature on frequency peak location and measurement for the application of ADC and DAC testing. Think 24 bit convertors. There is a much smaller literature providing window designs for interference suppression for testing done by the people who design 24 bit convertors to evaluate their device internal implementations. Those are the minimum sidelobe windows in "Windows Connections" (pages 6 and 12) at: http://www.abvolt.com/compdsp/presentations/Dalrymple/dbd.pdf Dale B. Dalrymple