On Jul 19, 9:58 am, Randy Yates <ya...@ieee.org> wrote:
>...
> There's also the landmark paper (seems no one quotes it
> anymore) that was published almost 30 years ago:
>
> @article{harris,
> title = "{On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform}",
> author = "{Harris, Frederic J.}",
> journal = "Proceedings of the IEEE",
> year = "1978",
> month = "January"}
>
> --
> % Randy Yates % "And all that I can do
> %% Fuquay-Varina, NC % is say I'm sorry,
> %%% 919-577-9882 % that's the way it goes..."
> %%%% <ya...@ieee.org> % Getting To The Point', *Balance of Power*, ELOhttp://home.earthlink.net/~yatescr
Reply by glen herrmannsfeldt●July 23, 20072007-07-23
Rick Lyons wrote:
(snip)
> I've thought about that before. My guess,
> if I had to guess, would be that Cooley's & Tukey's
> original FFT paper is the MOST referenced signal
> processing paper. Then comes harris' "Windows" paper
> as the 2nd-most referenced paper.
On Thu, 19 Jul 2007 12:58:39 -0400, Randy Yates <yates@ieee.org>
wrote:
(snipped)
>
>There's also the landmark paper (seems no one quotes it
>anymore) that was published almost 30 years ago:
>
>@article{harris,
> title = "{On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform}",
> author = "{Harris, Frederic J.}",
> journal = "Proceedings of the IEEE",
> year = "1978",
> month = "January"}
>
>--
>% Randy Yates % "And all that I can do
Hi Randy,
I've thought about that before. My guess,
if I had to guess, would be that Cooley's & Tukey's
original FFT paper is the MOST referenced signal
processing paper. Then comes harris' "Windows" paper
as the 2nd-most referenced paper.
(I wonder if that's true.)
See Ya',
[-Rick-]
Reply by Randy Yates●July 19, 20072007-07-19
R.Lyons@_BOGUS_ieee.org (Rick Lyons) writes:
> On Mon, 09 Jul 2007 13:07:44 -0700, dspguy2@netscape.net wrote:
>
> (snipped)
>>
>>The halfway point between fft bins is used since it represents the
>>worst case loss. At the halfway point the power in adjacent FFT bins
>>is equal (for symmetric windows). If the frequency is lower then more
>>power goes to the lower FFT bin and less to the upper FFT bin. The
>>opposite happens when the frequency is increased.
>>
>>Cheers,
>>David
>
> Hi,
> In case you're interested,
> there's a neat article, "FAST, ACCURATE FREQUENCY
> ESTIMATORS", by Eric Jacobsen and Peter Kootsookos
> in the "DSP Tips & Tricks" column, in the May 2007
> issue of the IEEE Signal Processing magazine.
>
> That article addresses the subject of this thread.
>
> See Ya',
> [-Rick-]
There's also the landmark paper (seems no one quotes it
anymore) that was published almost 30 years ago:
@article{harris,
title = "{On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform}",
author = "{Harris, Frederic J.}",
journal = "Proceedings of the IEEE",
year = "1978",
month = "January"}
--
% Randy Yates % "And all that I can do
%% Fuquay-Varina, NC % is say I'm sorry,
%%% 919-577-9882 % that's the way it goes..."
%%%% <yates@ieee.org> % Getting To The Point', *Balance of Power*, ELO
http://home.earthlink.net/~yatescr
Reply by Rick Lyons●July 19, 20072007-07-19
On Mon, 09 Jul 2007 13:07:44 -0700, dspguy2@netscape.net wrote:
(snipped)
>
>The halfway point between fft bins is used since it represents the
>worst case loss. At the halfway point the power in adjacent FFT bins
>is equal (for symmetric windows). If the frequency is lower then more
>power goes to the lower FFT bin and less to the upper FFT bin. The
>opposite happens when the frequency is increased.
>
>Cheers,
>David
Hi,
In case you're interested,
there's a neat article, "FAST, ACCURATE FREQUENCY
ESTIMATORS", by Eric Jacobsen and Peter Kootsookos
in the "DSP Tips & Tricks" column, in the May 2007
issue of the IEEE Signal Processing magazine.
That article addresses the subject of this thread.
See Ya',
[-Rick-]
Reply by ●July 9, 20072007-07-09
On Jul 9, 2:46 pm, "Ron N." <rhnlo...@yahoo.com> wrote:
> On Jun 30, 8:34 am, "qhash" <piotr.kuch...@vp.pl> wrote:
>
>
>
> > >On Jun 27, 6:07 am, "qhash" <piotr.kuch...@vp.pl> wrote:
> > >> Hi
> > >> ...
> > >> How should I apply this coherent gain coefficent ?
>
> > >> Regards,
> > >> Piotr
>
> > >Divide the windowed results by the coherent gain of the window.
>
> > >For bin centered tones, this should give the same value for all
> > >windows.
>
> > >For tones halfway between bins the value should be reduced from
> > >the bin centered value by the 'scallopping loss' parameter value
> > >from Harris' paper.
>
> > >Dale B. Dalrymple
> > >http://dbdimages.com
>
> > Thanks a lot ! The 'scallopping loss' solves the problem. However this is
> > still "black magic" as I do not fully understand the bin centered tones
> > idea. My data is a random data ,radiation gathered by the NA through
> > waveguide from the antenna. How can I know that those signals are not bin
> > centered ?
>
> Unless you are sampling synchronous to those signals,
> they are unlikely to be bin centered.
>
> > And why halfway ? Can't they be somewhere in-between ?
The halfway point between fft bins is used since it represents the
worst case loss. At the halfway point the power in adjacent FFT bins
is equal (for symmetric windows). If the frequency is lower then more
power goes to the lower FFT bin and less to the upper FFT bin. The
opposite happens when the frequency is increased.
Cheers,
David
Reply by Ron N.●July 9, 20072007-07-09
On Jun 30, 8:34 am, "qhash" <piotr.kuch...@vp.pl> wrote:
> >On Jun 27, 6:07 am, "qhash" <piotr.kuch...@vp.pl> wrote:
> >> Hi
> >> ...
> >> How should I apply this coherent gain coefficent ?
>
> >> Regards,
> >> Piotr
>
> >Divide the windowed results by the coherent gain of the window.
>
> >For bin centered tones, this should give the same value for all
> >windows.
>
> >For tones halfway between bins the value should be reduced from
> >the bin centered value by the 'scallopping loss' parameter value
> >from Harris' paper.
>
> >Dale B. Dalrymple
> >http://dbdimages.com
>
> Thanks a lot ! The 'scallopping loss' solves the problem. However this is
> still "black magic" as I do not fully understand the bin centered tones
> idea. My data is a random data ,radiation gathered by the NA through
> waveguide from the antenna. How can I know that those signals are not bin
> centered ?
Unless you are sampling synchronous to those signals,
they are unlikely to be bin centered.
> And why halfway ? Can't they be somewhere in-between ?
Yes. Amplitude estimation involves frequency estimation.
You need to estimate where the peak of the window
transform of your sinusoid of interest is located to
determine how far down the sides of that transform curve
your DFT result points are located. Then you can use
the inverse ratio (peak vs. data point locations) as your
amplitude correction factors. You might even want to
separately correct the points on either side and take
a weighted average.
> Also question about windowing. The gain I lose when I am using window
> different from rectangular one is not constant along the spectrum ?
Yes. The transform of any window (other than a 1 pt.
impulse) will not be completely flat in the frequency
domain. However, there are windows that are flatter
near the peak, thus giving correction factors closer
to 1.0, but more susceptible to certain kinds of
interference in exchange.
> So,
> does the coherent gain coefficent gives back the oryginal amplitude or it
> is burdened with some error ?
It is burdened with the need for a frequency dependent
correction factor.
IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
http://www.nicholson.com/rhn/dsp.html
Reply by ●July 9, 20072007-07-09
On Jun 30, 1:07 pm, dbd <d...@ieee.org> wrote:
> On Jun 30, 8:34 am, "qhash" <piotr.kuch...@vp.pl> wrote:
>
>
>
> > ...
> > So,
> > does the coherent gain coefficent gives back the oryginal amplitude or it
> > is burdened with some error ?
>
> > Best regards,
> > Piotr
>
> For tones that happen to fall at bin center, the coherent gain
> coefficient gives back the original amplitude. For frequencies that
> fall off the bin center, the error can be as great as the scalloping
> loss. The maximum error occurs if the frequency falls halfway between
> bin centers.
>
> Dale B. Dalrymplehttp://dbdimages.com
There's a description of amplitude correction (for sinusoidal tone
signals) in one of the B&K technical manuals which corrects for the
effects of windowing. First you determine the frequency by the peak of
the signal and the 2 surrounding FFT bins. Using these values you can
determine the frequency to more accuracy than the FFT bin width size.
Once you have the frequency you can then determine the amplitude
correction factor for that particular frequency. In the B&K manual
they only do it explicitly for something like a hamming window.
An generalized alternative is to precalculate the frequency/amplitude
corrections and put them in a table and interpolate to find the
corrections. This type of correction makes several assumptions.
1 - Signal of Interest is a pure sinusoid.
2 - High SNR, so noise contribution has little effect
3 - Leakage from other strong sinusoids is minimal.
An alternative is to use the Flattop window, which is designed so to
allow you to measure amplitude without any correction. Of course the
sidelobe behaviour isn't as good as some other windows.
Cheers,
David
Reply by dbd●June 30, 20072007-06-30
On Jun 30, 8:34 am, "qhash" <piotr.kuch...@vp.pl> wrote:
>
> ...
> So,
> does the coherent gain coefficent gives back the oryginal amplitude or it
> is burdened with some error ?
>
> Best regards,
> Piotr
For tones that happen to fall at bin center, the coherent gain
coefficient gives back the original amplitude. For frequencies that
fall off the bin center, the error can be as great as the scalloping
loss. The maximum error occurs if the frequency falls halfway between
bin centers.
Dale B. Dalrymple
http://dbdimages.com
Reply by qhash●June 30, 20072007-06-30
>On Jun 27, 6:07 am, "qhash" <piotr.kuch...@vp.pl> wrote:
>> Hi
>> ...
>> How should I apply this coherent gain coefficent ?
>>
>> Regards,
>> Piotr
>
>Divide the windowed results by the coherent gain of the window.
>
>For bin centered tones, this should give the same value for all
>windows.
>
>For tones halfway between bins the value should be reduced from
>the bin centered value by the 'scallopping loss' parameter value
>from Harris' paper.
>
>Dale B. Dalrymple
>http://dbdimages.com
>
Thanks a lot ! The 'scallopping loss' solves the problem. However this is
still "black magic" as I do not fully understand the bin centered tones
idea. My data is a random data ,radiation gathered by the NA through
waveguide from the antenna. How can I know that those signals are not bin
centered ? And why halfway ? Can't they be somewhere in-between ?
Also question about windowing. The gain I lose when I am using window
different from rectangular one is not constant along the spectrum ? So,
does the coherent gain coefficent gives back the oryginal amplitude or it
is burdened with some error ?
Best regards,
Piotr