Waterfalls

[brucek]

I've read some posts lately that I haven't really agreed with.

Point # 1 is regarding the effectiveness of equalization at low frequencies (15Hz-100Hz). The question posed is how can a parametric filter possibly correct room resonances. The assertion being that an EQ filter only lowers the relative SPL level in the room at that frequency, and as a result the ringing may be reduced since it drops into the noise, but it can't really correct the problem. Sorry, I don't agree..............................

Point # 2 deals with the practice of applying REW's smoothing feature to measured low frequency responses before addressing filter creation.

One of the most useful aspects of REW, and the one that seems to get ignored the most (especially with regard to the above) are the waterfall plots. Actually, I spend more time looking at LF waterfall and LF decay than I do frequency response graphs. They tell you so much more about the response of your room. How could they not, they add another dimension. The frequency response graphs completely ignore time. The effectiveness of smoothing can't be examined without a waterfall plot.

I performed a couple experiments that I think addresses the two points above.

Point # 1.
We've all looked at waterfall plots. They use the familiar horizontal axis of frequency and the vertical axis of SPL level that the frequency response graphs use, but they add a third dimension of time.

The waterfall is derived from the impulse response by shifting the impulse response window to the right by a proportion of the time range to generate each succeeding slice. It has to be generated before you can observe it, so you need to click the 'generate waterfall' for the measure you want to see..

The slice slider on the waterfall graph page shows you slices of time from the first response at zero time and then time is increased as you move to slice 30. So if you have the Time Range (ms) set to 300 ms and the resolution Window set to 300ms, each slice is 10msec after time zero. This shows what the microphone hears as time moves on from the initial sweep. If you have a resonance that tends to decay very slowly, you'll see it in the waterfall. This is what we're trying to reduce with the equalizer filters.

Whenever you create a waterfall plot of a measure, you can set the slider to zero and then slowly move it out to 30. This is the decay of the signal in the room. It will tell you quite a bit where the room resonances are.

Anyway, to better demonstrate that the behaviour of the BFD EQ filters have an effect in the time domain as well as the frequency domain (that matches the modal response of a room), I connected the BFD into a loopback cable of my soundcard and used this setup to take frequency response measurements.

Below is the result of a measurement of the BFD (with the filters bypassed) using the waterfall plot. The two dimensional frequency plot would show a simple flat line of course, but the waterfall plot adds the time dimension. Each slice in the waterfall is 10msec. After 130msec, the return is down in the noise.

Waterfall plot of a BFD with all filters bypassed.



Now I enter a single filter into the BFD. It is a 40Hz filter with a Gain of +15dB and a Bandwidth (BW) of 10, and I do a response measurement.

Below is the expected frequency response of the BFD with the single filter added.

Frequency Response plot of a BFD using a single filter of (40Hz, Gain +15dB, BW 10)



But now I look at the resulting waterfall plot of that single filter below.

Look familiar? Sure it does.

It looks like a room mode resonance of any REW measurement at subwoofer frequencies. And it should. It's because the EQ filter, just like the modal resonances of a room, has a time response that acts like a 2nd order biquad. If I apply an EQ filter with the same Q and opposite gain of a room mode, I would completely counteract the effect of the mode. See the time component of the filter (just like a room mode). It rings out, and still isn't in the noise after 300msec. You see, EQ filters don't just affect level. This is why they're so effective at equalizing at modal frequencies below 100Hz. Yes, it is listening position dependant, and only valid at the point where the response was measured, but because of the long wavelengths of low frequencies, the region around that area is fairly large. This is in opposition to higher frequencies where equalization is a bit of a waste of time, since the effective region is so small that eq is impractical.

Waterfall plot plot of a BFD using a single filter of (40Hz, Gain +15dB, BW 10)



As a side note, you can see what a completely terrible idea it is to add a gain filter to boost the level of a sub at low frequencies. You do nothing more than emulate a room mode at the gain frequency

So, if I enter a second filter into the BFD of (40Hz, -15dB, 10BW) to counteract the existing filter of (40Hz, +15dB, 10BW), the result is the measured response below. The room mode is completely nullified.

Waterfall plot plot of a BFD using a two filters of
(40Hz, Gain +15dB, BW 10) & (40Hz, Gain -15dB, BW 10)



And so, if we applied a counteracting filter in the BFD that matched a room's modes, the effects of the resonance is completely removed.

continued in the next post.......................

[brucek]

continued from above...............................

Point #2.

In keeping with the information in the post above, let's take the response of a BFD that uses a single filter of (40Hz, +15dB, 10BW) and let REW recommend a counteracting filter to remove it. Let's see if REW works....

Fairly obvious results, that REW recommends to add a counteracting filter of (40Hz, -15dB, 10BW). If I enter that filter, just as I previously did above in point #1, the result is a flat response with a flat waterfall. Below is the response graph of the room resonance filter and the REW filter recommended and the corrected response. The waterfall, of course, is the flat smooth response pictured above.

FREQUENCY RESPONSE OF A SIMULATED ROOM MODE AND REW's RECOMMENDED FIX


Now, lets add some smoothing to the response measurement of a BFD filter of (40Hz, +15dB, 10BW). This response represents a typical room mode from an actual measure. Instead of letting REW recommend a filter to counteract the mode, I'll add some smoothing to the response first and then see how REW does in recommending filters.

I'll enter those filters into the BFD and see what the resulting response is. I won't waste too much time on the frequency response graph since it doesn't really tell much of a story - I'll look at the waterfall and see if the filters I have applied after smoothing remove the resonance.

Below is the graph of the (40Hz, +15dB, 10BW) room mode with 1/2 octave smoothing added. The picture also shows the filter that REW recommends to enter into the BFD. No amount of manual intervention gets the corrected response any better.

FREQUENCY RESPONSE GRAPH OF A SMOOTHED SIMULATED ROOM MODE AND REW's RECOMMENDED FIX


Below is the picture of the BFD with the room resonance filter combined with the smoothed filter recommendation.


FREQUENCY RESPONSE GRAPH OF ROOM MODE AND REW's RECOMMENDED FIX AFTER FILTERS ENTERED INTO BFD


The revealing picture is the waterfall of course. It shows quite conclusively that filters optimized against a smoothed response will have settings that don't accurately match the room's modes. Look at the ringing out of that resonance.......

WATERFALL OF ROOM MODE THAT WAS SMOOTHED AND FILTER USED THAT REW RECOMMENDED



brucek

[Blaser]

These are very good remarks Brucek!! Bravo!
So, is it assumable that equalization can be more practical, cheaper, easier for room mode decay (ringing) as well as FR below say 80 Hz than room treatment? I am talking about a single seat of course.

[brucek]

So, is it assumable that equalization can be more practical, cheaper, easier for room mode decay (ringing) as well as FR below say 80 Hz than room treatment?

Well for sure. Certainly equalizing to remove modal resonances is what REW is all about. The listening area can be measured at mutliple positions and the results averaged if you like or you can choose a single position for the best results. The effective area will depend on the frequency of the mode. Acoustic treatment can improve the response over a wider area, but at those low frequencies <100Hz, the size of the treatment would be ridiculous. For less than 100Hz, use EQ. Above that, to about 500Hz (so I understand), use room treatment.

brucek

[thxgoon]

Very informative post, thanks!

So what in your opinion would be the best way to set up eq under 100hz. Would you not use the smoothing before assigning filters to the BFD?

[brucek]

Would you not use the smoothing before assigning filters to the BFD?

I would not use smoothing. The author of REW also highly recommends not to use smoothing before assigning filters.

I would take the raw measure and use REW to find peaks, assign filters and optimize. Enter those filters and then then see how the waterfall looks after a remeasure.

brucek

[toecheese]

Thank you Bruce! I disagreed with some recent things as well and you touched on some of them.

[Blaser]

Brucek,

I have once made the assumption that room treatment cannot be as effective as equalization below 80 Hz in another forum and I was strongly attacked by the members as well as by a very well know person (that I do respect a lot) in this industry.
You have encouraged me to make my own experiment in my room and to explain my point of view (based on real world measurements), and discuss it with those who might have some doubt.

Let's begin with a quick description of my room which is approx. 1800 cuft (5 m *3.6 m * 2.7 m). My subs are located on the front wall while I am seating about 0.7 m from the back wall. Before applying any eq. my problem was mainly the axial mode which I have measured to be about 18 db at 36 Hz approx.

Thanks to this wonderful and best forum that I know, I bought the FBQ 2496 which corrected this peak problem.... (but is it only the 36 Hz peak problem???, we'll see).

My analysis will be about the effect of equalization on the axial mode decay (36 Hz ringing) through LF waterfall(which will add the parameter of time as explained by Master Brucek). Take a look at the unequ. and eq. graphs below. For the sake of keeping things fair, I will keep the SPL of 36 Hz the same for both equ. and unequ. graphs.

Continues in following post....

[Blaser]

The reason why I kept the 36 Hz SPL the same for both graphs is because, the value after 300 ms can be too low or too high due to an initial smaller or higher SPL.

Now take a look at the LF waterfall for my unequalized room and equalized and both together. The difference is self-explanatory, although I have raised the amps output by 18 db after equalization (to keep the same value as the unequ. graph at 36 Hz.) the ringing is much less at 36 Hz, decay is faster and of course this will be less "boominess", and "tighter" sound.

Conclusion: Not only the equalized FR is of course of much supperior quality than the unequ. but LF waterfall graph is much better (about 12 to 14 db less SPL at 36 Hz after 300 ms), not to mention that the other frequencies are heard too, and the one note bass has left its place to a more pleasant listening experience.

Why is that? I don't know. Propably you Brucek may explain how this was electronically done.

Continues in next post...

[Blaser]

Some may mention that between 10 and 15 Hz, Waterfall is worst when equalised. I say no!
In the beginning I mentioned that for comparing data, we have to keep things fair. At 0 ms and at 10-15 Hz, the unequ. SPL is 52 db while it is 70 db with the equ. curve. The difference is 18 db (those that I have added by turning up the amps during the equ. graph). And something weird (is it) is happening: at 300 ms the 18 db difference is still the same, why? because no filter was used at these frequencies!! Anyway, any low decay at 20 Hz and below is wellcome for me

To confirm the above, below are the LF decay curves as well.

Some will claim that this is for only one seat. Again I say no. Check the very first post of Brucek about wave length of LF and you will note it does not change so much (due to their nature) unless the distance is great. Moreover, I am using dual subs aligned on the front wall, and this makes the FR quite similar at any lateral place of the couch, so these results will also apply to 4 or 5 seated people seating laterally in the room, and propable another raw for those who have larger rooms than mine (and of course larger room may sound even better).

How much money and room space give up (if possible at all) can we do similar results with bass trap?

Thank you!

[brucek]

Yeah, the equalization certainly seems to have nearly eliminated the resonance at 36Hz. The fact that the signal doesn't persist in the room after the other frequencies have gone, accounts for the better overall bass and a less muddy sound I'm sure.

You may even try taking successive measures while watching the small ringing out signal (shown in yellow) and manually tweak the FBQ a bit. Try a single click higher and lower for the parameters of frequency and bandwidth and see if you can get the center frequency and shape of the resonance any better (although it's quite good now-that's a very nice response).

I also wonder if a bit of sub phase or sub distance setting would help your crossover dip (shown in green)?



brucek

[Blaser]

Regarding the dip at 80 Hz, I am not too worried about it as it is not very wide. Nevertheless I will do some more tweeking later on.

[brucek]

In talking to blaser, he pointed out that I didn't explain too well in my last or original post the reason why an equalizer is helping the decay of the resonance and needed further explanation how this is done electronically?

Well, in my reading about 2nd order biquad filters, poles and zeros, and minimum phase systems, some of the assertions by the author of REW do make some sense in that regard.

I tried to explain this in my original post, but probably fell short since perhaps I don't fully understand it myself.

The modal response of a room acts exactly like a 2nd order filter and matches the BFD generated filters in all aspects. At modal frequencies, a room resonates in gain and Q exactly as if you fed a sub signal through a 2nd order parametric filter. This fact allow us to fashion an identical 2nd order filter with the opposite gain and bandwidth that matches the room mode so it will completely disappear (at the point of measurement).

This doesn't apply outside the low frequency range where signals are no longer considered minimum phase, where primary reflections (second order) from the walls, ceiling and floor arrive at the listening position anywhere in the room with a phase shift of quite a bit less than a cycle. So, the effective limit here of about 80Hz-100Hz is reasonable for equalization in most rooms...(an 80HZ signal has a wavelength of about 14ft)............


I suppose I could also add here that REW may also not suggest a filter for a peak that you think it should have tried to correct. This may be a result of the peak not having the attributes of a modal resonance (this is what REW is looking for). You'll likely find that if you examine the waterfall at that peak that REW ignored, there would be no ringing out in the time domain. There's nothing stopping you from adding your own manual filter into REW and then into the BFD. It would be wise to examine the waterfall after that though.

There also may be modal resonances very close together, perhaps as a result of equal lengh and widths in a room or other reflections. REW could have trouble finding these, so you may have to do it manually. It's tricky and requires a back and forth measurement and tweaking as you watch the waterfalls.

JohnM may refute any of my ramblings in this thread if they are misleading or plain dumb....


brucek

[JohnM]

Looks good to me, Bruce, and a nice job by blaser as well though there is scope for further improvement in the control of the modes around 36-40Hz in blaser's room. It will be interesting to see how the tweaks work out.

[Blaser]

Thanks John. When I have time, I'll try to tweek and see, but I don't expect much better result. Indeed equalization has already removed 12 db after 300 ms which is already very good,and propably not easily possible with any other method.

[Sonnie]

You guys are making my head hurt... really bad...

I'm gonna have to read this 3-4 times you know.

[SteveCallas]

Good stuff - excellent in room response blaser

[Chrisbee]

As I have frequently mentioned I boost at maximum at 20Hz to compensate for my high Fs 32Hz non-spec drivers. (AE IB15s)

BFD= 20Hz + 16dB BW= 120/60.

Here's a waterfall I generated from an older file. Extended to 1000ms and cropped to 80Hz to keep the interesting VLF area in view.



It seems that boosting with the BFD does indeed increase ringing.

[JohnM]

You won't see any ringing from the filter at that bandwidth setting, it is so broad it boosts a very wide range. The peaks in your measurement are most likely room-related. To see the effect of the filter alone connect the BFD in a loopback to your soundcard and measure it that way.

[Doug Plumb]

"You'll likely find that if you examine the waterfall at that peak that REW ignored, there would be no ringing out in the time domain."

This would be impossible. Its impossible to have a peak without the resonance or the ringing. Sharp peaks have sharp slow decay resonances. Dull peaks have quickly decaying responses or resonances.

If you know the frequency response then the impulse can be calculated then a waterfall can be calculated.

Really, the best way to look at response is with the single frequency response. The waterfall is prettier but of little practical use.

(I just had to say this after reading that, not interfering with REW thread)

[Blaser]

Chrisbee,

You need to compare your graph to the same initial 20Hz SPL (without BFD) and then compare after 1000ms. Otherwise you will never know.

Indeed, ringing at 20 Hz is not necessary a bad thing...It could be amazing

[thxgoon]

Wow, I envy all of you and your room response. I'm still working on mine but here is what I've go so far.... note this is going out to 933ms. At 300 virtually all frequencies were still there...



It's interesting to see on the waterfall that right before and after my lull at 56hz, there is are substantial nodes! I'm not too sure how to deal with this yet.

[brucek]

This would be impossible. Its impossible to have a peak without the resonance or the ringing.

Really, the best way to look at response is with the single frequency response. The waterfall is prettier but of little practical use.

Doug, we'll just have to disagree on just about everything in your post.

I wish I could find some better examples to show you that very similar peaks can have completely different persistence in time, but I could only find the response below (I've seen far better examples).

I find the waterfall plots very useful in identifying peaks that ring-out for a long time. I use REW to match that peak and reduce its ringing as low as possible. Other peaks that look very similar in the 2 dimensional frequency response plots that don't ring-out as much have nowhere near the impact to the sound.

Here's a quick example of two peaks that are very similar - at least they look that way using a simple frequency response plot. With the single slice 2 dimensional plot of frequency and amplitude, the two peaks look about the same.

Now examine what happens in a three dimensional plot when I move the slider to 30 slices to add time derived from the impulse response. One just keeps on going. And you hear that too. Using REW to match that room mode eliminates that ringing out in time..

Waterfalls are far more than pretty pictures.......

ONE SLICE


30 SLICES


brucek

[Doug Plumb]

"Doug, we'll just have to disagree on just about everything in your post."

I'm sorry to hear that. I program waterfall plots and have studied these response functions in detail as an engineering student. We spend about 4 courses per year for two years studying the response function in various courses from math to controls to DSP and analogue filtering.

NASA or any other company does not ever use waterfall plots to evaluate the response of their systems and the response of their control systems is similar to what we have here. I have never seen a waterfall plot in any serious controls theory, electric circuit theory paper or in any other form. Its never used for a reason - its useless !! They are only in audio, they look pretty but mean little. A well known Phd acoustician has agreed with me on this point and doesn't use them for the same reason.

They can obfusgate the situation when people mis interpret noise or the mathematical distortions in gating as an actual physical affect, as you have above.

Every single peak in the waterfall plot is due to a peak in the frequency response. If there is a section in the waterfall that displays a decaying portion without a peak in the frequency response then its noise or some other affect.

In some non mimimum phase systems you could possibly see a decaying part that does not show as a resonance in the first slice but the resonance must appear in later slices. This is very unlikely and absolutely unlikely in a modal region room response.

[Blaser]

Well...at least the ears do not lie. There is not need for a very sophisticated program to check for HT audio stuff. Anyway, the waterfalls in REW is a very useful program, and if correctly understood (I do not mean you don't) and utilized will with no doubt help enhance ringing (at low freqs of course).

Did you take the time to see the improvement clarfied by the waterfalls taken in my room...They definitely confirm the HUGE improvement that was done in my room. And at least, this is a practical measurment...