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Sr. Member
Posts: 163
Reply with quote  #16 
As usual, you provide a well thought out set of test data. I wasn't aware of the previous thread and work you had already done.

Jack Frarey wrote a series of papers on signal analysis which helped me to better understand the subtleties of the whole FFT process. I tried to Google the papers but could not find online that I could share w/o compromising copyright issues. If you are a member of VI, you can find them on their website.

The conclusions you find are very similar to what Jack wrote about in his articles.
One of his primary points was the choice of the window (essentially a bandwidth filter) used and its effect on the amplitude output for a given random noise input. Was all your testing using a Hanning window?

I certainly don't want to beat this discussion to death....I just find it interesting and perhaps it provides some useful thought for various applications for our forum readers. As you stated, it is usually more important to identify  the "frequency"of a peak vs. accuracy of the amplitude for typical condition-based spectrum. I believe the choice of of the window function and LOR probably outweighs increasing the number of averages.

Users beware, analysis and conclusions noted above does not apply for captured transient data; which can be greatly affected by the choice of windows, lines of resolution and Fs.

Thanks again for your work and the comments from all the members
Jim P

Sr. Member
Posts: 651
Reply with quote  #17 

Yes, my test used Hanning window (you can search my attachment for Hanning and see related comments and the call to Matlab Hanning function embedded in one of my user-defined functions that occurs immediately before each fft).

I don't focus much on the magnitude aspect of windows since usually it's the trend. Spectral leakage into adjacent bins due to time windowing is present no matter what window we choose, and the Hanning is a nice balance to minimize this (much better than rectangular window).  The spreading for a given window is a multiple of bin width.   Choosing the higher resolution option of one long FFT rather than averaging multiple smaller FFT's gives the same window-based multiple of a smaller bin width, so frequency can be determined with more precision. But we already knew that… the single long FFT gives better frequency resolution than the average of multiple shorter FFT outputs.  

The higher averages definitely hurts your ability to identify a peak with precision.  The higher averages doesn't help anything at all if you have a strictly periodic signal. The advantage comes if you have a signal that is not strictly period and includes a broadband component that results in a noise floor.  The higher averages approach will make that noise floor less "bumpy", while the higher resolution option lowers the noise floor but makes it more bumpy.

Some related discussion here:

Excerpt from above link:

Periodogram method


The periodogram method divides the signal into a number of shorter (and often overlapped) blocks of data, computes the squared magnitude of the windowed (and usually zero-padded) DFT… of each block, and averages them to estimate the power spectral density. The squared magnitudes of the DFTs of L  possibly overlapped length-N  windowed blocks of signal (each probably with zero-padding) are averaged to estimate the power spectral density…


For a fixed total number of samples, this introduces a tradeoff: Larger individual data blocks provides better frequency resolution due to the use of a longer window, but it means there are less blocks to average, so the estimate has higher variance and appears more noisy. The best tradeoff depends on the application. Overlapping blocks by a factor of two to four increases the number of averages and reduces the variance, but since the same data is being reused, still more overlapping does not further reduce the variance. As with any window-based spectrum estimation procedure, the window function introduces broadening and sidelobes into the power spectrum estimate. That is, the periodogram produces an estimate of the windowed spectrum

It seems basically the same as I've said, describing the same tradeoff.  

I showed a plot of broadband noise contrasting the two approaches. They show similar comparison between their Figure 2 (single long=1024 fft) vs their Figure 3 (multiple averaged shorter FFTs).  It again shows the bumpy floor for the high res approach and the smoother floor with averaging.  A small difference is the underlying noise is bandlimited / low frequency in their demonstration, in contrast to mine which was  white noise uniform across the spectrum.

Reviewing what they did vs what I did, one important difference.  They are working with power spectral density, whose magnitude would correspond to the the square of our vibration FFT. Accordingly they average the power spectral density.  To accomplish an equivalent averaging, I would have had to take square-root-of-sum of squares of the indvidual FFT outputs (rather than arithmetic average that I did).  It makes me wonder which method is used in an analyser. I'm not sure, but I don't think the differences would be dramatic.

One thing I ran across somewhere while googling before I posted this was an explanation for using overlap.  One of the links mentioned the overlap method was an attempt to compensate for the "data lost" in the windowing process, which tends to destroy or limit the impact of the data at each end of the individual time window.  If you have for example 25% overlap, then the data in the first quarter and last quarter of each time record gets counted in two different FFT's… compensating for the fact that that data shows at reduced magnitude after windowing.  That sort of makes sense.  But in that case, there wouldn't be much benefit ever going above about 25% overlap.

Sorry for long post, second time in a row. It was not necessarily a response to you (Jim P) - just rambling about some more things that came to mind. Brevity was never my strong suit.


Sr. Member
Posts: 384
Reply with quote  #18 
Good stuff guys. Thank you all for taking the time.
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