waterfall plot 1

[anands78]

I neeed to know the mathematics behind the generation of waterfall plots. I have the time domain data (say some 2^n points gathered every 1 second thru the running speed range of the machine) and would like to convert that to the frequency domain and construct the waterfall plot from it.
Any books/answers will be very helpful.

Thanks

 

[GregLocock]

Well to do it bass ackwards a waterfall is just a staggered array of 2d plots, preferably with hidden line removal.

Rather more important is what the plots are. You get from time series data to spectra by using FFTs, typically. Most usually you do a waterfall of power spectra, or the modulus of the spectrum(Z), against time or speed(Y), against frequency (X).

Here is an excellent on-line introduction that will get you going.

http://cp.literature.agilent.com/litweb/pdf/5952-8898E.pdf

Here's one with more details about FFTs

http://www.science.unitn.it/~bassi/Signal/NInotes/an041.pdf

Here is an excellent introduction to the philosophical details of FFTs. Ignore the details of wavelets, the stuff on Fourier is worth the price of admission

http://engineering.rowan.edu/~polikar/WAVELETS/WTtutorial.html

Excel has a built in FFT analysis, in one of the toolpaks. It is a bit hard to get right, but it does work. With a bit of cunning Excel will plot waterfalls as well.



Cheers

Greg Locock

 

[MikeyP]

Top links Greg. Thanks

M

 

[anands78]

Hi Greg

Thanks for the post. Ive read those application notes atleast 10 times each. Let me state my question clearer. Say that I have the time domain data for every second as I stated before. I convert this to the freq domain with an FFT function. We now have the signature of the machine at various speeds. If I now need to plot the waterfall, is it just a matter of display (or visual representation )concerned with the particular software that I am using(say excel or mathcad..)or is there any Math involved there?

The reason is if I use mathcad I cant use one of those 3D graphs. And if I use a 2D graph, I have one "X" value for which there are many "Y" values..

Thanks

 

[IRstuff]

You don't have a single x value for many y values. The waterfall plot plots time(x), frequency and magnitude(z).

If you already have the data, there is no more math involved. Each FFT is assigned to its time slot and you then plot the 3-D data.


TTFN

 

[MachineryWatch]

No math involved. It is just a matter of plotting in a way that is most "enhancing" to the data. As Greg mentioned the hidden line blocking is nice. Many times skewing the plots (offsetting each new spectrum slightly to the side of the previous one) can also be effective. Many new waterfall displays are being presented with ways to enhance amplitude appearances with color, etc. and even some that interpolate data in the gaps between calculated spectra to give a more flowing and continuous look to the data (which I guess does enter into the math required realm).

Hope this helps. It really depends on how sophisticated your display program is. Most of the canned programs that come in vibration analysis software packages have some nice features but also have room for improvement.

Skip Hartman

http://www.machinerywatch.com

 

[GregLocock]

You can do this in mathcad. Just put each spectrum as a row in a matrix and plot the matrix.



Cheers

Greg Locock

 

[anands78]

Thanks a lot guys..