- May 21, 2017
- Corpus Christi, TX
My AV System
- Preamp, Processor or Receiver
- Yamaha RX-Z9 A/V Receiver
- Universal / Blu-ray / CD Player
- Pioneer BDP-23FD Blu Ray Player
- Front Speakers
- Canton Karat 920
- Center Channel Speaker
- Canton Plus D
- Surround Speakers
- Canton Plus D
- Surround Back Speakers
- Realistic Minimus 7 (front EFX speakers)
- Front Height Speakers
- Yamaha YDP2006 Digital Parametric EQ (front mains)
- Rear Height Speakers
- Yamaha YDP2006 Digital Parametric EQ (subs)
- Adcom ACE-515 (for power management)
- Video Display Device
- Yamaha DT-2 (digital clock display)
- Audio Control R130 Real Time Analyzer
- Remote Control
- Stock Yamaha Remote
- Streaming Subscriptions
- Pioneer PDP-6010FD 60" Plasma TV
Adventures in Waterfalling
Understanding Signal Levels in Time-Domain Graphs
Understanding Signal Levels in Time-Domain Graphs
Once upon a time in a land far, far away, the capability to generate waterfall graphs was limited to expensive software programs available primarily to professional speaker designers and acoustics engineers.
However, the advent of affordable measurement platforms like TrueRTA, Room EQ Wizard and others has made these powerful analytical tools available to the general public, most of whom have no formal training or experience in the relevant sciences. As a result we now have a curious mix of enlightenment and chaos: Someone downloads a sophisticated measurement platform, and in a few days he's an expert dispensing wisdom to the even less-informed on the audio forums. Do a search on “rew waterfall graph images” and you’ll find all kinds of crazy-looking stuff.
Over at Home Theater Shack you’ll find an old thread on waterfall graphs, dating back to the early days of the REW program, that runs for 17 pages. A thread doesn’t go on for 17 pages unless there is a lot of debate over conflicting ideas and interpretations, not to mention people just trying to get a handle on this new (to them) topic. And I’d have to include myself in that category as well, at the time. The ever-patient and affable John M. endured our pathetic musings without throwing up his hands and calling us all a bunch of idiots. At least not publically.
It’s surprising the amount of confusion and misinformation that still surrounds the subject of low frequency ringing and waterfall graphs after all these years. Equally problematic is the question of how to address ringing, and even more so, how to determine if it has been improved. It's common to see people confuse say, mere gain changes (as we often get with equalization) with an improvement (or not) in ringing.
For instance, I’ve seen threads where people were happy with the audible results of equalizing their subwoofer, but were disappointed that it didn’t get them an improvement in ringing. And others who, after boosting at 20 Hz to compensate for their sub’s lack of extension, were annoyed that equalization actually introduced ringing – completely unmindful of the fact that such an adjustment will make a time-domain graph appear worse than before. On the flip side, I’ve seen others who claimed to have achieved a 300-400 ms improvement in ringing after subwoofer equalization, which is patently impossible.
Sadly, these folks are in good company, as such contradiction can be found even among those who should know better. On the Web you can find manufacturers of equalization equipment, as well as companies that specialize in acoustics, present “before and after” time-domain graphs that claim to show an improvement in ringing, that actually do not. I’ll show some tragic examples of the type in Part 2 of this piece.
Decay Speed vs. Decay Rate
A quick explanation for those who may have no idea of what any of this is: “Ringing” is a succinct term that refers to the time it takes a bass signal to fade down to the room’s noise floor after the signal stops. Measurements of the decay duration are typically presented in time-domain graphs such as waterfalls and spectrograms.
To start, let's clarify a few definitions. In the following discourse, when I refer to "decay time" I mean the time it takes a signal to fade away, relative to its gain or loudness. For example, an 80 dB signal will quite naturally fade down to the noise floor in less time than a 95 dB signal.
When I refer to "rate of decay" or “decay rate” I mean how fast the sound decays: If we have 85 dB signals in two separate rooms and one fades to the noise floor in 300 ms, and the other in 200 ms, the latter has a faster "rate of decay.”
It should probably be noted at this point that the accepted professional benchmark for determining audio signal decay in a room is known as RT60. RT60 (RT = reverberation time) refers to the time it takes latent reflections to drop 60 dB after the signal has been shut off. Unfortunately, RT60 measurements are mainly relevant in auditorium spaces, not the small rooms where we typically have our systems, for a number of reasons.
For starters, RT60 measurements are accomplished with specialized equipment and measurement devices, not the omnidirectional measurement mics or hi-fi speakers we use with REW and similar platforms. In addition, RT60 measurements typically are not full range and do not factor the highest frequencies, or the lowest, where we are most interested in learning about the in-room behavior of our subwoofers. Furthermore, the waterfall or spectrogram graphs we use will seldom have a full 60 dB of signal from peak to floor anyway. (Note: Here is a good link with more information on RT60 for those interested, including a nifty video showing how the measurements are taken.)
Another problem is that RT60 measurements incorporate both “decay time” and “decay rate,” as you can see from the graph linked above. However, for our purposes we need to look at these two things separately.
So with RT60 off the table as the gauge for defining the low frequency decay behavior of a home theater room, I’m forced to come up with some terms of my own – hence “decay time” and “decay rate.” I don’t pretend that these are legitimate scientific definitions, but hopefully clarifying a difference between the two will help keep the discussion understandable and making sense.
In addition, when you see the term "ringing" being used, there is (again) typically no delineation between the “time” and “rate.” You’ll often see people say things like, “After doing ‘xxx,’ an increase [or decrease] in ringing can be observed,” with no indication if they mean “decay time” or “decay rate.” (I suspect that most of them don't know a difference exists.)
Confused already? Don't feel bad – lacking that background in the relevant sciences myself, it took me years to sort this stuff out. Let's try to untangle it.
That Old Graph Magic
Probably the most common source of confusion on this topic is misunderstanding the effect that signal levels (i.e. gain or SPL) have on a waterfall or spectrogram. Here’s a waterfall graph from a thread at Home Theater Shack some years back:
Graph 1: 105dB Waterfall
Looks pretty scary, huh? Notice that the signal is peaking at nearly 110 dB. Now, let’s look at the same measurement with the signal reduced to peak at 85 dB:
Graph 2: 85dB Waterfall
Wow. Just like magic it looks much better, doesn’t it? As you can see, merely reducing the signal level makes for a noticeably “better” waterfall graph, because a quieter signal will obviously fade away quicker than the louder one:
Graph 3: Signal Level and Delay Time
But that is not the same thing as improving the decay rate, as you see happening on the right side of this graph:
Graph 4: Signal Level and Rate of Decay
Now let’s look at the relation between room modes and signal level. This probably isn’t the best explanation, but a room mode is a build-up of bass energy that causes a substantial increase in level (gain or SPL) at a certain frequency. As we’ve seen, any increase in signal level nets an increase in decay time: A room mode takes longer to fade away merely because it is louder than the rest of the signal. Again, this is not to be confused with the decay rate.
However – what distinguishes a room mode from a “regular” peak in frequency response is that it will also display a longer decay rate in addition to the increase in SPL.
What can we do about the huge “sore thumb” signal level of the room mode? Enter the equalizer. An equalizer is merely a device that alters signal gain at specified frequencies.
Graph 5: Baseline (purple) vs. Equalized Frequency Response (black)
With a parametric equalizer we can set a precise filter – bandwidth, frequency and negative gain value – that counteracts the mode and basically robs it of energy. We can see the effect with this "before and after" that features a nasty mode at 55.7 Hz. Counteracting the mode with a precisely-set parametric filter eliminates its audible and unpleasant “boomy” effect.
Graphs 6 and 7: Room Mode Before and After PEQ
So by reducing the level (gain) of the mode, the equalizer brought its decay time, as well as its decay rate, back in line with what the room is naturally exhibiting.
Here's another example. In this comparison, a parametric filter was set for a mode at 41.9 Hz. This time with the second graph, the level of the signal after equalization was raised to match the SPL reading the mode was displaying before being equalized. In other words, 41.9 Hz are at the same SPL in both graphs. Naturally, increasing the signal level in the second graph makes it look worse overall (as discussed above). However, we can clearly see that after equalization, the frequency where the mode was located (41.9 Hz) now displays a significant improvement in rate of decay.
Graph 8: Baseline Waterfall
Graph 9: Waterfall with 42 Hz Filter
So we can see in both the presentations above that the room mode’s rate of decay has indeed improved after equalization. Please note however, it has not improved beyond the room average. At the of the day, this is the best that can be achieved with electronic equalization. It’s pretty much an iron law.
How Ringing is Significantly Improved
Why is that? The next thing to understand is that ringing is the same to low frequencies as audible reverberation (or echo) is to the upper frequencies. Both have to do with the rate of decay: If you have a room with a lot of hard surfaces, it has a lot of reverberation because the sound bounces around all over the place and takes a long time to fade away. Add some room treatments, furniture, carpet etc. and the reverberation virtually vanishes. Why? Absorption. The furnishings and treatments absorb the sound waves and thereby the reverberation is truncated – i.e. the rate of decay the "live" room exhibited has been radically stunted. It should be self-evident that an equalizer is no cure for a "live" room that has lots of echo and reverberation, nor is any other electronic device.
Graph 4: Signal Level and Rate of Decay
In the same manner, absorption is required to improve low-frequency ringing – by that I mean the signal decaying at a faster rate, irrespective of its SPL. Typically this means bass traps or something similar. An equalizer can only make adjustments in gain levels to problematic frequencies; it cannot absorb acoustical energy. It can make a waterfall graph "look" better to the untrained eye by reducing the signal level of peaking frequencies, but again – that doesn’t necessarily mean there was an improvement in the rate of decay.
So, how do you determine from a "before" and "after" waterfall graph if you have actually realized an improvement in ringing? It’s simple: Just study the spacing between the horizontal lines. Each horizontal line indicates a "slice" (fraction) of time as the signal decays from its "starting point" until it falls to the graph's floor. So, if there is a real and factual improvement in ringing – i.e., if the signal in an "after" waterfall graph is actually decaying faster than in the "before" graph – there will be wider spaces between the horizontal lines.
This is clearly evident in the graphs below that show ringing in a room with and without bass traps. Note the dramatic difference above 140 Hz that absorption makes.
Graph 10: Ringing in an Untreated Room
Graph 11: Ringing in a Treated Room
Courtesy of Real Traps
You simply can't get this effect with an equalizer – again, it can't absorb acoustic energy. Don't get me wrong, equalizers are great tools for what they do. Personally I love them. I have lots of equalizers. But you have to know and respect their limitations.
Slices and Levels
Obviously it’s easy to use a waterfall graph to gauge the effects of ringing when bass traps have been added, especially if you add a lot of them. However, gauging the effects of equalization is different, because equalizers merely address ringing by reducing the level of a modal peak. For example, let's revisit this graph shown earlier in this post, where an EQ filter eliminated a 55.7 Hz room mode:
Graphs 6 and 7: Room Mode Before and After PEQ
This time take a closer look at the spacing of the slices seen both outside the circle, and inside where the mode was equalized. Note that the signal level (SPL) of the area below 45 Hz is something on the order of 10-12 dB higher than the signal level above 45 Hz. Yet, the spacing of the slices is virtually the same across the board. This should sufficiently demonstrate once again that once you've eliminated the room modes, you can't equalize to further "improve" ringing. All you're doing at that point is making gain (signal level) changes, not improving the decay rate .
Aside from studying the spacing of the slices, the best way to show if EQ improved ringing in a room mode is gain matching the baseline signal with the equalized signal. Since equalizing the mode will bring a gain reduction at the offending frequency, and hence a better-looking waterfall graph, it’s easy to be fooled into thinking there was an improvement in ringing whether there actually was one, or not. As such, the offending frequency in the “after” graph should be level-matched to the baseline measurement, as seen above in Graphs 8 and 9 above. That will make it easy to see if the decay time of the mode actually improved. This is especially important if you’re using spectrograms instead of waterfalls: Since they have no slices to study, it’s the only way to tell that a mode’s long “tail” has fallen in line with the rest of the graph.
It should be further clarified not every peak in measured frequency response is a room mode, as this graph shows:
Graph 12: Room Modes vs. Room Peaks
We can clearly observe from the long decay “tails” that there are room modes at 40, 62, and 90 Hz. But notice the peak at 120 Hz. You can see that it is at a much higher level than the peaks at 40 and 62 Hz, but its rate of decay is significantly faster than those two. This is because 120 Hz is not a room mode. Addressing that peak via EQ would certainly bring an improvement in perceived sound quality, but not an improvement in the decay rate, as would be observed by examining the slice spacing.
This is the situation people face when trying to use equalization to improve ringing where there are no apparent room modes, as you can see below 30 Hz in the next graph. The only "improvement" you'll see will merely be the effect of the signal level being reduced by the equalizer, so you're just chasing your tail. All you’ll get is less bass.
Graph 13: No Room Modes