Skip to main content

Replies sorted oldest to newest

I believe the flat-top window is set up to give the best possible estimate of the magnitude of a peak. It doesn't do particularly well at estimating the frequency of a peak or separating it from neighboring peaks separated by a small number of bins.

There is also "rectangular window" which is different than flattop window. Sometimes used for bump test transient if it decays within the window.

Hanning is good for general purpose analyis. Good frequency separation and reasonable magnitude estimation.
RM
quote:
Flat top window is good for amplitude measurement (1% inaccuracy)


Shouldn't we have some assumptions here, such as there is a single frequency and no others nearby? Then the question becomes, how do you now there is only one peak? Use a different window or resolution.

To say 1% accuracy also implies that the peak does not vary more than 1% in amplitude. This is typical of all field data Roll Eyes .
RM
Dear all,

Thanks to all for the valuable comments & appreciated it very much.

Quote: It gives good resolution but not that good amplitude. There may be amplitude error upto 16%. Flat top window is good for amplitude measurement (1% inaccuracy) but poor resolution.

Does it means that with good resolution,flat top window is preferred (1% inaccuacy) on amplitude measurement? So it is good for trending with no much amplitude error measured.
RM
quote:
Originally posted by Kids:
Dear all,

Thanks to all for the valuable comments & appreciated it very much.

Quote: It gives good resolution but not that good amplitude. There may be amplitude error upto 16%. Flat top window is good for amplitude measurement (1% inaccuracy) but poor resolution.

Does it means that with good resolution,flat top window is preferred (1% inaccuacy) on amplitude measurement? So it is good for trending with no much amplitude error measured.

The flattop is good for determining the magnitude of single peaks. It is miserable for determination of frequency of the peak or separating closely spaced peaks. Usually it is not critical to know the exact magnitude of a single peak (most people trend on overalls). But if you did want to trend the magnitude of a single peak, flattop would be best. But it is not good for anything else. And if you use it you still need another spectrum for frequency resolution.

The only place I use Flattop window is for part of current signature analysis. In that case I need a good reading of motor fundamental current magnitude to help me estimate motor load and slip (tells me where to look for the sidebands). BUT I don't use flattop to look for the pole pass sidebands... I use Hanning.
RM
Attached
Slide 1 = current signature, Hanning window, 6400cpm Fmax, 6400 lines, 1 average.
Slide 2 = same signal (same machine at almost same time), Hanning window, 6400cpm Fmax, 6400 lines, 1 average.
Slide 3 = Impulse response of Hanning window and flattop window

In slide 1 (Hanning) we see a large peak 2.23A (ct secondary) at 3597 cpm, with adjacent sideband of interest 0.0037A at 3522 cpm.

In slide 2 (Flattop) we see the same signal. It now looks like large peak 2.393A at 3598cpm with sidebands 0.0062 at 3524cpm.

The parameter of interest for current signature analysis is ratio of magnitude of large peak to magnitude of small peak. We have big variability in magnitude of that small peak (0.0037 or 0.0062).... will affect our ratio,.

Why is that variability? I assume it is because of the contribution from the main peak which results in a very broad bulged noise floor spreading out from 3598 and extending well past 3524 in the Flattop. So the bin at 3524 is seeing a vector addition of the 3524 sinusoid and the bulged noise floor from the 3598 in the Flattop and is reading too high..

So I would use the following numbers:
Frequencies: from Hanning – 3597cpm and 3522cpm
3597 magnitude – from Flattop – 2.393
3524 magnitude – from Hanning – 0.0037
As mentioned before, I also use the Flattop line frequency magnitude 2.393 multipled by CT ration to determine actual current from which I can estimate slip as a double-check that I'm looking at true pole pass sidebands.

Take a look at slide 3 which is impulse response of these windows. If we input a pure sinusoid to this finite window, then resulting FFT should be "samples" of this continuous curve at a frequency interval of one binwidth. Since the frequency duration is not in anyway selected to synchronize with the sinusoid frequency, the samples may end up exactly at 0,1, 2, 3, ... or at 1.1, 2.1, 3.1 etc or any set which is separated by exactly 1 bin width. There will always be one sample within 0.5 bin widths of zero which is the place where the magnitude of the curve is 1. (That is also the explanation for the name "flattop"... it is flat in frequency domain... not in time domain... rectangular window is the one that's flat in time domain).

The flattop as shown in slide 3 as you can see is very flat (almost horiziontal slope) for a long distance as it crosses the vertical axis at 0 bin widths, so even if you reach the worst case alignment where you sample this curve at 0.5 bin widths, the amplitude resolution is still very good near 1.0 (assuming no other peaks around).

The downside of flattop window as shown in slide 3 generally has a broader envelope than the spectrum, especially out at 75bins so it is in agreement with what we saw on the spectrum.... this is what forced our small peak to read higher than actual (we suspect).

Now one thing I notice is the Hanning does better at avoiding noise from the big peak polluting the little peak for the region where little peak is up to about 5 bins out from big peak and also more than 15 bins out. But from 5-15 the flattop actually does better. Who'd of thunk it.

Another thing doesn't quite make sense: at 75 bins out the bulged noise floor from flattop should not be more than 2E-5 times the fundamental. But from my spectrum it looks to be maybe 1E-3 times the fundamental. I was expecting when I wrote this up that the bulge in noise floor of actual flattop would agree with theoretical, but it doesn't. Maybe someone can explain to me why it isn't. I'm guessing maybe it has something to do with the nature of my signal?..... one more post with another attachment to follow.

Attachments

RM
Last edited by Registered Member
Attached are theoretical calculations to derive these curves and associated parameters for a variety of windows (comparison flattop and Hanning at the end). I guess there's a possibility I made an error somehow in generating the curves... it has been awhile since I created them, but my memory is they matched the textbooks pretty well.

At any rate I'm not going to waste my weekend worrying about it but anyone is welcome to comment if they can explain to me why our flattop FFT bulging noise floor seems so much higher than the theoretical one.

Attachments

RM
Last edited by Registered Member
Noise floor is determined by the actual noise floor level and the frequency resolution the spectrum. The flat top window gets better amplitude accuracy at the expense of frequency resolution. Essentially, with the flat top window, you don't have enough frequency domain resolution to reduce the noise floor enough below the level of the side band of interest to make the measurement with confidence. Use the hanning window and don't worry about the accuracy. At the worst an in the lowest probablility case, the reading will be 15% down from the peak. There are ways to improve the amplitude accuracy of a hanning windowed specturm but, unless you can change the programming of you analyzer, kknowing this won't help you.
RM
I agree with you Hanning does 99% of what we want. I take advantage of Flattop only to get most exact measurement of fundamental current magnitude which is needed to estimate motor loading and slip to give highest confidence I am looking at correct sideband corresponding to pole past frequency. And in that case I only use it in conjunction with Hanning which gives me my frequency information and my sideband amplitude information.

I agree I used the term bulging noise floor loosely... I was referring to the extended skirt around a large peak whose origin is presumably mostly leakage from that one large peak (although exact origin in question... noise or leakage as discussed below)

The one question I mentioned... in my flattop spectrum of slide 2 you can clearly see a symmetric skirt on both sides of 3600cpm that would seem to be the leakage from that one very large peak. If it were unrealted to the peak, it would not be symmetric around the peak like that. Additionally it is a factor of 10 higher than similar "floor" or "skirt" of Hanning. But the rate of decrease of the Flattop skirt as we move away from the center seems much slower than the theoretical one shown on slide 3 which shows that at 75 bins out, the skirts should be 2E-5 or lower.

I double checked myresults against similar one in Wikipedia
http://en.wikipedia.org/wiki/F...%28comparsion%29.png
This is the same plot except they use log/log scale for magnitude/freq, whereas I used log/lin scale. If you look between 70 and 80 bins you can eyeball around -92db for flattop. That means a ratio 10^(-92/20) = 2E-5 which agrees with mine. So my curve was right. But still the conflict with measurement remains (it is not 2E-5 down... it is only 1E-3 down). I cannot explain it as "noise floor" because noise floor would not be symetric about 3600cpm. My best explanation is that the signal is not truly sinusoidal and maybe there is something else going on besides leakage of a pure sinusoid signal that results in this spreading.... after all we know we know the signal is not pure sinusoid at 36000... we also have sidebands which represent additional components beyond the sinusoidal 3600component.... maybe there is more complex perturbation of this 3600 signal than we know about that doesn't show up as discrete sidebands but instead shows up as spreading of the skirt. But that's not exactly satisfying to me.
RM
Last edited by Registered Member

I add here a simple Windowing Demo from RITEC.

In this simulator, the user can generate single or dual frequency signals, and apply several different types of windows on them to view the effects of non-bin-centered data, whereby leakage of energy to adjacent bins occurs; a result of processing finite-duration records.

There are several types of windows available in this simulator including: Hann (Hanning / Raised Cosine), Bartlett, 4-term Blackman-Harris, Flat-Top, and Hamming windows. The spectral content is amplitude corrected with the appropriate window Amplitude Correction Factor.

https://www.ritec-eg.com/Libra...se-Factor-basic.html

RM

Add Reply

×
×
×
×
Link copied to your clipboard.
×