mdeale@cosmos.acs.calpoly.edu (Myron Deale) (10/17/89)
Hello, given a series of data points in the time domain, eg. a bunch of samples from an A/D converter (like the new 12/16-bitter sigma-delta ADC from Moto), I can understand what an FFT will show me and sort of understand what a power spectrum calculation will show, but what would a "waterfall display" show? what is its advantage? -Myron // mdeale@cosmos.acs.calpoly.edu
sampson@attctc.Dallas.TX.US (Steve Sampson) (10/17/89)
I saw one (I think) on a special concerning the Voyager spacecraft. Each time line is drawn under the previous. Generally it looked like a TV on a blank channel except for the Voyager return telemetry drawing a line down the screen (slight angle). I guess then they would be used to find a signal buried in the noise? Hope this helps with one idea.
mhorne@ka7axd.WV.TEK.COM (Michael T. Horne) (10/17/89)
In a recent article by mdeale@cosmos.acs.calpoly.edu (Myron Deale): > > Hello, > given a series of data points in the time domain, eg. a bunch of samples > from an A/D converter (like the new 12/16-bitter sigma-delta ADC from Moto), > I can understand what an FFT will show me and sort of understand what a > power spectrum calculation will show, but what would a "waterfall display" > show? what is its advantage? > Typically the waterfall display is used to watch slowly varying spectra or for catching some spectral event. It provides you with a past history of spectra by placing them on the display in such a way that allows you to view several spectral scans (or FFT interations) at the same time. It is often used in weak signal detection (e.g. the intelligence community often uses it for spread-spectrum signal detection). Depending on how much spectral history is displayed, you can easily see signal changes in the spectrum of interest when they are placed on the display in a line-by-line (raster style) fashion. Some spectrum analyzers take advantage of color display technology by translating the magnitudes of a spectral sweep into colors that are then displayed on the CRT in a line-by-line raster scan. With a large number of these `color-keyed' scan lines on the display you can quickly detect changes in spectral content, magnitude, etc. Other spectrum analyzers with non-color displays draw the spectral sweeps on the CRT in a manner that makes it look somewhat like a 3D surface. > -Myron > // mdeale@cosmos.acs.calpoly.edu Mike mhorne@ka7axd.wv.tek.com
gd@milkfs.istc.sri.com.uucp (Greg DesBrisay) (10/18/89)
A waterfall display of FFTs draws every new FFT curve on the screen slightly below and "in front" of the last curve. The effect is that you get a 3-dimensional looking display with frequency as the x axis, amplitude as the y axis, and time as the z axis. The third axis provides an very effective way to display time-varying signals. For example, Ray Vincent, formerly of SRI, who now works as an independent consultant and professor at the Naval Post Graduate School uses a system with a waterfall display to locate and identify all sorts of radiated electrical noise. Each different type of noise source has it's own distinct three-dimensional pattern on a waterfall display. Greg
news@ge-dab.GE.COM (USENET News System) (10/18/89)
> >A waterfall display of FFTs draws every new FFT curve on the screen >slightly below and "in front" of the last curve. The effect is that From: harrison@sunny.DAB.GE.COM (Gregory Harrison) Path: sunny!harrison Another type of transform can be used to obtain the time-frequency display of a waterfall display. This is the Wigner Distribution. The Wigner Distribution performs an operation on the input time series, then does an FFT. The input time series is sampled starting at progressive times in the data, as in the FFT method. What the Wigner Distribution, WD does is to provide greater time-frequency localization of the components in the signal. In a FFT, as the FFT length is increased, the frequency resolution is increased, but the ability to discern changing frequencies decreases. As series of FFTs are displayed on the waterfall, the ability to discern the time of presence of a signal also decreases (I think this is also a direct function of the length). This results in signals being smeared in time and frequency, if they are nonstationary. The Wigner calculates the Power spectrum at a certain time, not over a range of time. The length of the WD can be increased arbitrarily in order to obtain frequency resolution, without introducing smearing. For instance, the WD of a chirp signal is very close to a nice clear delta function that increases in frequency as time goes on. The FFT technique yields a messy, smeared, wide band of frequencies increasing in frequency as time goes on. The WD introduces artifacts not in the FFT, but a large number of these artifacts can be eliminated using the Wigner-Ville Distribution, WVD. The Wigner provides better high frequency response than the FFT, as seen when analyzing speech with identical length FFTs and WDs. The Wigner operates by creating a kernal: k(i) = s(i)s*(N-i) for i = 1 to N, k(i) is the kernal, and s(i) is the input sequence. Then the following: WD(f) = abs(FFT(k(i))) There are ways to make the WD provide real output for real input, and thus perform 2 WD in one FFT essentially doubling throughput. A very good reference is: B. Boashash and P.J. Black, "An Efficient Real-Time Implementation of the Wigner-Ville Distribution," IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-35. No. 11, Nov. 1987 P.S. This is what I'm doing my thesis on. Greg Harrison My opinions are not intended to reflect those of GE.
aglew@urbana.mcd.mot.com (Andy-Krazy-Glew) (10/19/89)
"Waterfall display" sounds like what I have seen [*] called a "cascade
plot". Usually they were a representation of how the frequency
content of a signal changes over time - ie. they were FFT spectra
taken over successive intervals, in a pseudo-3D representation.
Draw FFT#1 at the baseline.
Draw FFT#2 at the baseline + dX,dY; choose dX,dY so that you get very
nearly parallel lines, and not too much detail is hidden behind
the peaks (actually, varying dX,dY interactively can be very useful
too. Sort of like looking at a signal in perspective - but different).
Ditto FFT#3, 4, 5...
This gives you a 3D looking plot where you can see the frequency components
changing over time. Patterns emerge very clearly.
In my own work I have used cascade plots to inspect computer performance
data, like variations in kernel profiles according to workload. Occasionally
I have wanted '4D' or greater type cascade plots, where the underlying
data is more than 2D, varying over time.
[*] Hell, I'll be honest: "I have seen" == my Dad uses; my Dad is one of the
Vibrations Analysis wizards that kept the Canadian Navy going on the
oldest destroyers in the world. I keep thinking that some knowledge
engineer should interview him to build an expert system for this sort
of maintenance and signal processing, now that he's retired.
--
Andy "Krazy" Glew, Motorola MCD, aglew@urbana.mcd.mot.com
1101 E. University, Urbana, IL 61801, USA. {uunet!,}uiucuxc!udc!aglew
My opinions are my own; I indicate my company only so that the reader
may account for any possible bias I may have towards our products.