# Waterfall Window



## MarkusBonk (Jun 5, 2010)

Hi

Can someone please explain the parameters one can input into the waterfall graph (time range and window) and what the effect of changing them is? The help does not elaborate on their effect and simply states at the end: " Best results are obtained when the window is smaller than the time span."

I have thought until now that a waterfall was the equivalent of waiting until the loudspeaker/room had reached then steady state frequency response and then switching off the input.

The "time range" I have interpreted as being the first x ms bit of the decay I am interested in. i.e. I get 10ms slices if I set it to 300ms or 20ms slices if set to 600ms etc.

The "window" is what is causing confusion.








The above shows the default settings in the waterfall control (time range=300ms, window=300ms) This seems to claim that there is a mode/noise at 36.3Hz which has dropped to 62dB after 300ms








The above is the same measurement as before but with the window set to 600ms. Now we have something that looks like modes again but we have shifted to 35Hz and 67dB.

This I find very confusing. One or both graphs must be wrong or they are simply showing me different information which I cannot interpret. 








Same measurement same time range=300ms now the window is 1200ms. I definitely don't understand what is happening/what I am being shown. Why does one decay faster than the other? What will setting a shorter window allow me to see? I am setting a long window time to determine the frequency of the mode








Same window as above, now with the time range set to 600ms.

Another point I always wonder about is why the peaks after say 300ms don't match the peaks at t=0, they tend to smear off to one side?

Confused.
H.


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## Barleywater (Dec 11, 2011)

Waterfall plots are result of reading impulse response result with time window. The window starts out centered (hopefully) at the impulse response peak, this is frequency response slice at t=0. The window is sequentially moved along the impulse response by (Time Range)/(number of slices) for each additional frequency response slice. The slices are stacked to form waterfall plot. The window size determines frequency resolution with trade off: bigger window resolves lower frequencies at expense of temporal resolution. So to see what a tweeter is doing smaller time range, smaller window, and the opposite for woofers. When looking for room reflections compromises must be made.

It would be nice feature if REW allowed user selection for more slices, but with practice 30 slices covers a lot of ground.

Hope this clears up some of the confusion.

Andrew


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## MarkusBonk (Jun 5, 2010)

Thanks Andrew, but no, I am still as ignorant as before.


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## JohnM (Apr 11, 2006)

There are 2 main factors that affect the appearance of the waterfall plot, the time range and the window settings. To understand the effect they have, it is first necessary to understand how the waterfall plot is produced, elaborating on Andrew's comments above.

Each slice of the waterfall plot shows the frequency content of a windowed part of the measurement. 'Windowed' means we take the measurement and multiply each sample in it by the value of a window, whose shape we can choose. Here is an example of an impulse response showing the original impulse, the window shape and the windowed response. 








Here is a zoomed in view of the early part, where the effect windowing has on the windowed (lighter red) trace can be seen.








After the frequency content of the first windowed part of the impulse response has been obtained it is plotted as the first slice of the waterfall. The window is then moved along the response and the process is repeated for the next slice. The amount the window moves is determined by the time span and the number of slices, so that the data for the last slice is from a section of the impulse response that is later than the first by the time range - for example, if the time range was 300ms and there were 31 slices there would need to be 30 shifts of the window (the first slice has no shift) so each slice would be from data obtained after moving the window 10ms along the impulse (300/30).

The window has a left hand side and a right hand side. In the plots above, the left hand window is a Hann type that ends at the peak of the impulse. The right hand side is a Tukey 0.25 (which means that for 75% of its width it is flat, then the remaining 25% is a Hann window). The overall width of the window (left side plus right side) determines the frequency resolution of each slice of the waterfall. The shape of the window, and particularly the shape and width of the left hand side, affects the way features of the response are smeared out in time. 

To understand this, imagine a rectangular window and a perfect impulse, that has one sample at 100% and all other samples zero. As long as that single 100% sample is within the span of the window the frequency response will be a flat line. As soon as the left edge of the window goes past the 100% sample that slice and all slices after it will have no data in them (all the samples will be zero) so the waterfall would disappear off the bottom of the plot. That is, in the time domain, a faithful representation of how that perfect impulse response looks - and in general for any response a rectangular window gives the best time resolution, but that comes at a price. The price is in the frequency domain behaviour, i.e. the shape of the frequency response in slices of the waterfall. In real impulse responses, that are spread out over time, using a rectangular window would create a sharp step at the left hand edge of the windowed data. That sharp step would cause ripples in the frequency response, obscuring the actual frequency content. To avoid those ripples, a tapered window is used to smoothly attenuate the samples, but now a feature that does actually have a rapid change in the impulse response will linger on in the waterfall, because it will not entirely disappear until the whole left hand window has gone past it.

REW's waterfalls have been aimed at examining room resonances. To help make those resonances easy to see in the response, a wide left hand window is used - its width is half the setting entered as the "Window" time, the right hand window has a width equal to the window time. However, that means that increasing the Window setting increases the frequency resolution (the main reason for wanting a longer window) but also stretches the response out in time, due the increased left hand window width. That is not very helpful, as it means the time range has to be increased to get back to a useful view of the behaviour.

I have made a few changes to the waterfall behaviour in my current development build to improve things. Firstly, the left hand window width is specified independently, using a setting labelled "Rise Time". I have also added a control to select how many slices the waterfall should have (up to 100), and a control to select the smoothing to apply to each slice. I have also added a CSD mode, which keeps the right hand end of the window at a fixed point and only moves the left side, which is useful when examining cabinet or tweeter resonances over very short time spans. Those changes will be in the next beta release, probably in a few weeks time, but in the meantime here are some plots to show the effects of the settings. 

The first plot shows the downside of using a rectangular window on the left hand side. This plot has rise time 50ms, window 300ms, time range 300ms, Rectangular window on the left and Tukey 0.25 on the right. You may notice that the first 7 or 8 slices are almost identical, because the left hand edge of the window is moving towards the peak but hasn't reached it. The big rise at the lowest frequencies is an artefact caused by the step that the rectangular window creates in the windowed data.








Here is the same data but using a Hann window for the left hand side. The frequency response of each slice is much easier to see.








Finally, this is the same as the previous plot but the Window setting has been increased to 1000ms for greater frequency resolution.








Hope that helps.


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## MarkusBonk (Jun 5, 2010)

Hi John,

Thank you for the explanation. I need a while to run this through my brain, but haven't the time at the moment. I am off for a couple of weeks, but when back I will let you know if anything is still not clear.

Thank you again


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