Reply by Rick Lyons February 16, 20122012-02-16
On Wed, 15 Feb 2012 12:42:25 -0800 (PST), dbd <dbd@ieee.org> wrote:

>On Feb 15, 10:05 am, glen herrmannsfeldt <g...@ugcs.caltech.edu> >wrote: >> dbd <d...@ieee.org> wrote: >> >> (snip) >> >> > Gee Glen, I wasn't aware of anyone who used coherent averaging to >> > balance car tires, Can you you give us an example of someone who does? >> > Or is this meant as an example of average incoherence? >> >> There is a device that spins the tire for a while, then stops, >> ... >> I have seen the machines, but never >> looked inside. >> >> -- glen > >So where's the DSP? Rick's question was about FFTs: > >On Feb 14, 5:53 pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote: >> By the way my question of "On what sort of signals >> can you perform coherent averaging of multiple FFTs?" >> was a serious question.
>Your average still seems to be incoherent to the question. > >Dale B. Dalrymple
Hi Dale, For me, glen's posts are relavent because I was wondering about applications that require repeated capturing of time-domain signals where those various signals are phase-coherent. [-Rick-]
Reply by Rick Lyons February 16, 20122012-02-16
On Tue, 14 Feb 2012 20:50:10 -0800 (PST), dbd <dbd@ieee.org> wrote:

>On Feb 14, 5:53 pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote: > >> >> By the way my question of "On what sort of signals >> can you perform coherent averaging of multiple FFTs?" >> was a serious question. Yes, I know that the >> blocks of time samples must be 'phase coherent' >> for sucg coherent analysis. >> What I was wondering was *EXACTLY* what sort of >> signals there are, which we might want to analyze, >> that would be 'phase coherent'. No real-world, >> information-carrying, signal that I know of meets >> that criteria. The only such signals I can think of >> that could be analyzed, spectrally, with coherent >> averaging is the sinusoidal input signals used by >> guys who are measuring the performance of A/D >> converters using the FFT. >> >> See Ya', >> [-Rick-] > >Machine vibration analysis is a common application of synchronous >averaging. In practice the sampling is performed synchronously with a >shaft rotational rate or a tachometer signal is used to supply >information to resample to a synchronous sample frequency that can >follow speed variations. There is better coverage in the IEEE Trans on >Instrumentation and Measurement than in the Signal Processing >literature. A good search term might be "synchronous sampling". Gas >turbines in jet planes, helicopters and stationary power generation >plants are monitored and maintained with instrumentation that uses >synchronous (re)sampling. Helicopter rotor track and balance >instruments will measure imbalance and tell the maintenance operator >how much weight to put how far out on which blade to balance the >rotor. Gas turbines are balanced in the same manner. Much large >rotating industrial machinery gets such attention. > >As to the application of averaging to windowed power data, the >following documents are a good practical discussion: > >Windows to FFT Analysis (Part I) >Technical review No. 3 - 1987 >This article demonstrates how the analogy between DFT/FFT (Discrete >Fourier Transform/Fast Fourier Transform) analysis and filter analysis >(analogue or digital) can be used to better understand the >applications of different weighting functions used in DFT/FFT. The >filter characteristics of the most commonly used weighting functions >(also called windows) are illustrated and discussed with respect to >their use in various practical applications of system and signal >analysis. The mathematical formulations of the analogy as well as >rigorous details of the article will be given in the Appendices in >Part II of this article to be published in Technical Review No. >4-1987. >And p29 Signals and Units > >at: >http://bruel.ru/UserFiles/File/Review3_87.pdf >or >www.bksv.com/doc/bv0031.pdf >registration required at www.bksv.com, and worthwhile if you want to >learn about applied dsp > > >Windows to FFT Analysis (Part II) >Technical review No. 4 - 1987 >Technical Review 1987-4 Use of Weighting Fuctions in DFT/FFT Analysis >(Part II); Acoustic Calibrator for Intensity Measurements SystemsPart >II of the article "Use of Weighting Functions in DFT/FFT analysis" >contains the following Appendices referred to in Part I of the article >A: Analogy between filter analysis and DFT/FFT analysis, >B: Windows and figures of merit, >C: Effective Weighting of overlapped spectral averaging >D: Experimental Determination of the BT product for FFT-analysis using >different weighting functions and overlap, >E: Examples of User Defined Windows, >F: Picket Fence Effect > >at: >www.bksv.com/doc/bv0032.pdf >registration required at www.bksv.com, and worthwhile if you want to >learn about applied dsp > >Bruel&Kjaer have extensive application notes and technical papers on >DSP algorithms used in their long history of marketing sensors and >instruments. > >Dale B. Dalrymple
Hi Dale, Thanks for all the info!! [-Rick-]
Reply by dbd February 15, 20122012-02-15
On Feb 15, 10:05 am, glen herrmannsfeldt <g...@ugcs.caltech.edu>
wrote:
> dbd <d...@ieee.org> wrote: > > (snip) > > > Gee Glen, I wasn't aware of anyone who used coherent averaging to > > balance car tires, Can you you give us an example of someone who does? > > Or is this meant as an example of average incoherence? > > There is a device that spins the tire for a while, then stops, > ... > I have seen the machines, but never > looked inside. > > -- glen
So where's the DSP? Rick's question was about FFTs: On Feb 14, 5:53 pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:
> By the way my question of "On what sort of signals > can you perform coherent averaging of multiple FFTs?" > was a serious question. > ...
Your average still seems to be incoherent to the question. Dale B. Dalrymple
Reply by glen herrmannsfeldt February 15, 20122012-02-15
dbd <dbd@ieee.org> wrote:

(snip)

> Gee Glen, I wasn't aware of anyone who used coherent averaging to > balance car tires, Can you you give us an example of someone who does? > Or is this meant as an example of average incoherence?
There is a device that spins the tire for a while, then stops, and tells the user where and what weight to put on. It is called dynamic balancing, much preferred to static balancing which doesn't spin the tire. Also, it knows how much to put on which side, which you can't tell from static balance. Sounds just like your other examples, but I suppose it could also use incoherent averaging. As I said before, though, for incoherent averaging you usually have to know that the phase is random. If it isn't, you can get artifacts, pretty much like aliasing. I have seen the machines, but never looked inside. -- glen
Reply by dbd February 15, 20122012-02-15
On Feb 14, 11:50&#4294967295;pm, glen herrmannsfeldt <g...@ugcs.caltech.edu>
wrote:
> dbd <d...@ieee.org> wrote: > > (snip) *Rick's question on coherent averaging* > > > There is better coverage in the IEEE Trans on > > Instrumentation and Measurement than in the Signal Processing > > literature. A good search term might be "synchronous sampling". Gas > > turbines in jet planes, helicopters and stationary power generation > > plants are monitored and maintained with instrumentation that uses > > synchronous (re)sampling. Helicopter rotor track and balance > > instruments will measure imbalance and tell the maintenance operator > > how much weight to put how far out on which blade to balance the > > rotor. Gas turbines are balanced in the same manner. Much large > > rotating industrial machinery gets such attention. > > It is also done for car tire balancing, which is closer to > home for most of us. > > Same principle, though. > > -- glen
Gee Glen, I wasn't aware of anyone who used coherent averaging to balance car tires, Can you you give us an example of someone who does? Or is this meant as an example of average incoherence? Dale B. Dalrymple
Reply by glen herrmannsfeldt February 15, 20122012-02-15
dbd <dbd@ieee.org> wrote:

(snip)

> There is better coverage in the IEEE Trans on > Instrumentation and Measurement than in the Signal Processing > literature. A good search term might be "synchronous sampling". Gas > turbines in jet planes, helicopters and stationary power generation > plants are monitored and maintained with instrumentation that uses > synchronous (re)sampling. Helicopter rotor track and balance > instruments will measure imbalance and tell the maintenance operator > how much weight to put how far out on which blade to balance the > rotor. Gas turbines are balanced in the same manner. Much large > rotating industrial machinery gets such attention.
It is also done for car tire balancing, which is closer to home for most of us. Same principle, though. -- glen
Reply by glen herrmannsfeldt February 15, 20122012-02-15
Rick Lyons <R.Lyons@_bogus_ieee.org> wrote:

(snip)
>>> What 'noise' is increased when you average multiple FFT >>> magnitudes? Why would computing ten 4096 FFTs take more >>> processing time than computing a single 40960-point FFT?
(snip)
> Good gosh you're 'quick on the trigger'. > I was hopin' to hear pierson's answers to my > questions. In any case, thanks glen.
> By the way my question of "On what sort of signals > can you perform coherent averaging of multiple FFTs?" > was a serious question. Yes, I know that the > blocks of time samples must be 'phase coherent' > for sucg coherent analysis.
> What I was wondering was *EXACTLY* what sort of > signals there are, which we might want to analyze, > that would be 'phase coherent'. No real-world, > information-carrying, signal that I know of meets > that criteria. The only such signals I can think of > that could be analyzed, spectrally, with coherent > averaging is the sinusoidal input signals used by > guys who are measuring the performance of A/D > converters using the FFT.
(snip, I previously wrote, and moved down from above)
>>Consider, though, the way radio-astronomy is done. Signals >>are collected from widely spaced dishes, along with exact timing. >>The signals can then be combined with the appropriate phase, >>to get the equivalent of a very large antenna. Without the >>timing, the signals would have to be considered incoherent.
I believe this is a good example. By adjusting the phase, they change the direction that they are looking. I believe that phased array radar should also qualify. But also important are the cases where you don't want them to average coherently. One interesting one is the effect of multiple UTP ethernet cables in the came conduit. If they count as incoherent, then the noise adds as sqrt(N), but since all run at (about) the same frequency, that isn't so obvious. -- glen
Reply by dbd February 15, 20122012-02-15
On Feb 14, 5:53 pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:

> > By the way my question of "On what sort of signals > can you perform coherent averaging of multiple FFTs?" > was a serious question. Yes, I know that the > blocks of time samples must be 'phase coherent' > for sucg coherent analysis. > What I was wondering was *EXACTLY* what sort of > signals there are, which we might want to analyze, > that would be 'phase coherent'. No real-world, > information-carrying, signal that I know of meets > that criteria. The only such signals I can think of > that could be analyzed, spectrally, with coherent > averaging is the sinusoidal input signals used by > guys who are measuring the performance of A/D > converters using the FFT. > > See Ya', > [-Rick-]
Machine vibration analysis is a common application of synchronous averaging. In practice the sampling is performed synchronously with a shaft rotational rate or a tachometer signal is used to supply information to resample to a synchronous sample frequency that can follow speed variations. There is better coverage in the IEEE Trans on Instrumentation and Measurement than in the Signal Processing literature. A good search term might be "synchronous sampling". Gas turbines in jet planes, helicopters and stationary power generation plants are monitored and maintained with instrumentation that uses synchronous (re)sampling. Helicopter rotor track and balance instruments will measure imbalance and tell the maintenance operator how much weight to put how far out on which blade to balance the rotor. Gas turbines are balanced in the same manner. Much large rotating industrial machinery gets such attention. As to the application of averaging to windowed power data, the following documents are a good practical discussion: Windows to FFT Analysis (Part I) Technical review No. 3 - 1987 This article demonstrates how the analogy between DFT/FFT (Discrete Fourier Transform/Fast Fourier Transform) analysis and filter analysis (analogue or digital) can be used to better understand the applications of different weighting functions used in DFT/FFT. The filter characteristics of the most commonly used weighting functions (also called windows) are illustrated and discussed with respect to their use in various practical applications of system and signal analysis. The mathematical formulations of the analogy as well as rigorous details of the article will be given in the Appendices in Part II of this article to be published in Technical Review No. 4-1987. And p29 Signals and Units at: http://bruel.ru/UserFiles/File/Review3_87.pdf or www.bksv.com/doc/bv0031.pdf registration required at www.bksv.com, and worthwhile if you want to learn about applied dsp Windows to FFT Analysis (Part II) Technical review No. 4 - 1987 Technical Review 1987-4 Use of Weighting Fuctions in DFT/FFT Analysis (Part II); Acoustic Calibrator for Intensity Measurements SystemsPart II of the article "Use of Weighting Functions in DFT/FFT analysis" contains the following Appendices referred to in Part I of the article A: Analogy between filter analysis and DFT/FFT analysis, B: Windows and figures of merit, C: Effective Weighting of overlapped spectral averaging D: Experimental Determination of the BT product for FFT-analysis using different weighting functions and overlap, E: Examples of User Defined Windows, F: Picket Fence Effect at: www.bksv.com/doc/bv0032.pdf registration required at www.bksv.com, and worthwhile if you want to learn about applied dsp Bruel&Kjaer have extensive application notes and technical papers on DSP algorithms used in their long history of marketing sensors and instruments. Dale B. Dalrymple
Reply by Rick Lyons February 14, 20122012-02-14
On Wed, 15 Feb 2012 00:57:18 +0000 (UTC), glen herrmannsfeldt
<gah@ugcs.caltech.edu> wrote:

>Rick Lyons <R.Lyons@_bogus_ieee.org> wrote: >> On Tue, 14 Feb 2012 06:46:07 -0800 (PST), pierson wrote: > >> [Snipped by Lyons] > >>>Yes, and so does coherent averaging (as well as increase your S/N). >>>I use incoherent averaging all the time too, but only due to practical >>>matters because I can average 10 4096 point FFT's easily, but cannot, >>>due to system limitations, perform one big 40960 point FFT. > >(snip) >> just so Marc2050 doesn't misunderstand your >> post, it would be nice to have a little more >> explanation here. > >> On what sort of signals can you perform coherent >> averaging of multiple FFTs? > >Well, the easy answer is when the phase is known. >And for incoherent averaging, the phase has to be random. >That is, you have to have reason to believe that there >is not a simple phase relationship even if you don't know it. > >There is the rule from optics, for coherent sources, add >the amplitude, for incoherent sources, add the intensity. > >(Which ignores the fact, mentioned by Jerry not so long ago, >that there is a coherence length. It isn't always a yes or no, >but sometimes a maybe.) > >> I don't know if there is such a thing as a 40960-point >> FFT, but how would averaging ten 4096 FFTs be related >> to a single 40960-point FFT? > >Well, considering that longer FFTs are built from >shorter ones, it shouldn't matter. If the phase is known, >then you can add up the 4096 point transforms appropriately. > >Following the "add the intensity," in the case of the FFT >you want to add magnitudes. (Or RMS add the amplitude.) > >> What would force you to use windowing when averaging >> multiple FFTs? > >That is an interesting question. I recently went to a Tektronix >demonstration of their new oscilloscope with built-in digital >spectrum analyzer. It seems that the default (but selectable) is >to use the Kaiser window before doing the FFT. Since you can't >rely on the signal being periodic in the transform length, you >need windowing. Windowing reduces the effect from the periodic >boundary condition, that occurs at the beginning and end >of the transform. > >That seems a separate question from averaging, but maybe not. > >> What would force you to perform multiple FFTs on overlapped >> time-domain data? > >One obvious case is when the data comes in that way, or >when it is buffered that way. (You may fill a buffer, then slowly >write it out. And again, not know the phase relationship.) > >Consider, though, the way radio-astronomy is done. Signals >are collected from widely spaced dishes, along with exact timing. >The signals can then be combined with the appropriate phase, >to get the equivalent of a very large antenna. Without the >timing, the signals would have to be considered incoherent. > >> What 'noise' is increased when you average multiple FFT >> magnitudes? Why would computing ten 4096 FFTs take more >> processing time than computing a single 40960-point FFT? > >Averaging N incoherent samples decreases the noise (uncerainty) >by sqrt(N). Averaging coherently, if the phase is properly >considered, should reduce it by N. If the phase isn't accounted >for, you can get very far off. > >-- glen
Hi glen, Good gosh you're 'quick on the trigger'. I was hopin' to hear pierson's answers to my questions. In any case, thanks glen. By the way my question of "On what sort of signals can you perform coherent averaging of multiple FFTs?" was a serious question. Yes, I know that the blocks of time samples must be 'phase coherent' for sucg coherent analysis. What I was wondering was *EXACTLY* what sort of signals there are, which we might want to analyze, that would be 'phase coherent'. No real-world, information-carrying, signal that I know of meets that criteria. The only such signals I can think of that could be analyzed, spectrally, with coherent averaging is the sinusoidal input signals used by guys who are measuring the performance of A/D converters using the FFT. See Ya', [-Rick-]
Reply by glen herrmannsfeldt February 14, 20122012-02-14
Rick Lyons <R.Lyons@_bogus_ieee.org> wrote:
> On Tue, 14 Feb 2012 06:46:07 -0800 (PST), pierson wrote:
> [Snipped by Lyons]
>>Yes, and so does coherent averaging (as well as increase your S/N). >>I use incoherent averaging all the time too, but only due to practical >>matters because I can average 10 4096 point FFT's easily, but cannot, >>due to system limitations, perform one big 40960 point FFT.
(snip)
> just so Marc2050 doesn't misunderstand your > post, it would be nice to have a little more > explanation here.
> On what sort of signals can you perform coherent > averaging of multiple FFTs?
Well, the easy answer is when the phase is known. And for incoherent averaging, the phase has to be random. That is, you have to have reason to believe that there is not a simple phase relationship even if you don't know it. There is the rule from optics, for coherent sources, add the amplitude, for incoherent sources, add the intensity. (Which ignores the fact, mentioned by Jerry not so long ago, that there is a coherence length. It isn't always a yes or no, but sometimes a maybe.)
> I don't know if there is such a thing as a 40960-point > FFT, but how would averaging ten 4096 FFTs be related > to a single 40960-point FFT?
Well, considering that longer FFTs are built from shorter ones, it shouldn't matter. If the phase is known, then you can add up the 4096 point transforms appropriately. Following the "add the intensity," in the case of the FFT you want to add magnitudes. (Or RMS add the amplitude.)
> What would force you to use windowing when averaging > multiple FFTs?
That is an interesting question. I recently went to a Tektronix demonstration of their new oscilloscope with built-in digital spectrum analyzer. It seems that the default (but selectable) is to use the Kaiser window before doing the FFT. Since you can't rely on the signal being periodic in the transform length, you need windowing. Windowing reduces the effect from the periodic boundary condition, that occurs at the beginning and end of the transform. That seems a separate question from averaging, but maybe not.
> What would force you to perform multiple FFTs on overlapped > time-domain data?
One obvious case is when the data comes in that way, or when it is buffered that way. (You may fill a buffer, then slowly write it out. And again, not know the phase relationship.) Consider, though, the way radio-astronomy is done. Signals are collected from widely spaced dishes, along with exact timing. The signals can then be combined with the appropriate phase, to get the equivalent of a very large antenna. Without the timing, the signals would have to be considered incoherent.
> What 'noise' is increased when you average multiple FFT > magnitudes? Why would computing ten 4096 FFTs take more > processing time than computing a single 40960-point FFT?
Averaging N incoherent samples decreases the noise (uncerainty) by sqrt(N). Averaging coherently, if the phase is properly considered, should reduce it by N. If the phase isn't accounted for, you can get very far off. -- glen