Waterfall plots 101

[Coytee]

My hope is we can start/have a discussion on waterfall plots and get into the basics of what they mean and how they can (or should be?) interpreted.

Perhaps someone can post a "perfect" waterfall for a reference, explain the different sections of it (do they even have sections?) and then post a simple, yet "bad" waterfall so the differences between the two can be clearly pointed out and explained as to what the differences mean, how they might be created and how you might hear and then possibly fix them.

I spoke with MAS the other night and he spent some time explaining them to me. All I had to go on was my memory of what I'd seen them look like and thought it might be a lot better if we could have a "101" class on them.

Anyone willing to put them up and get into it?

[DrWho]

Here's one from Ethan's site:

-(http://www.ethanwiner.com/acoustics.html)

Neither is perfect, but I think it's obvious which is better. Ideally, you would have a flat line across the back (indicating a flat frequency response at time = 0) and then everything will decay at the same rate (none of these fingers sticking out at particular frequencies).

However, the ideal length and rate of the decay is a very subjective condition, but it's not something one has much control over anyway. I might argue that different decay rates at different frequencies might sound better too, but that would be a broadband thing - it should be widely accepted to get rid of ringing at particular frequencies.

[Deang]

I can only imagine what that conversation sounded like -- I'm breaking out in hives just thinking about it.

[mas]

Sad to say, it wasn't nearly as stimulating as a hearty discussion over which capacitor will cause less damage to the sound than another...

But what would be quite interesting would a discussion of their storage of energy and the damage they impart with regards to factors such as, say, the damping (or lack of) of a speaker motor assembly. ;-)

[Coytee]

Neither is perfect, but I think it's obvious which is better.

Mike... you need to approach this like you're talking to a 6 year old... hmm... ok... as per my wife, maybe a 4 year old.

Ideally, you would have a flat line across the back (indicating a flat frequency response at time = 0) and then everything will decay at the same rate (none of these fingers sticking out at particular frequencies).

That does infer to me that the top one is "better"... so I'm catching up with ya

Edit: I DO mean to say the BOTTOM one as I was typing this without the pics in front of me...seems the bottom one doesn't have the line sticking out as far??

However, the ideal length and rate of the decay is a very subjective condition,

Can't the effects/images be exaggerated to the extreme to at least show "blatently bad" and "acceptably good" images/concepts??

but it's not something one has much control over anyway. I might argue that different decay rates at different frequencies might sound better too, but that would be a broadband thing - it should be widely accepted to get rid of ringing at particular frequencies.

[]

[Coytee]

Dean..as an aside, did you get the spreadsheet I emailed you yesterday?

[Deang]

Sad to say, it wasn't nearly as stimulating as a hearty discussion over which capacitor will cause less damage to the sound than another...

Don't think I've ever been involved in a discussion about that. All decent measuring caps are probably about the same in that respect. I only care about the end result, and practical experience shows me that different types impact the voicing of the speaker. From where I'm sitting, the one that causes the least amount of 'damage' is the one that doesn't ruin the tonal balance of the speaker.

But what would be quite interesting would a discussion of their storage of energy and the damage they impart with regards to factors such as, say, the damping (or lack of) of a speaker motor assembly. ;-)

I've been taught that resistors divorce an amp's damping from the driver, but I don't really understand why that is. I've never heard the argument applied to capacitors. Seems to me they are a necessary evil. Even if using active filtering, if the amplifiers don't have protection relay circuitry -- you need capacitors in the signal path to block DC. That stuff isn't good for speaker motor assemblies either.

I'm sure you'd have no trouble twisting me up into a pretzel on any of these issues, I'm just a dumb audiophile ya know.

[Deang]

Sure did Richard, saw it this morning when I came in. Thanks a bunch for that.

[DrWho]

lol Richard, you're outta control []

Think of it this way....fingers are bad. Every finger you see is a single note that resonates, where all the frequencies without fingers are notes that don't resonate. Picture some newb bass guitar player trying to learn how to play scales. I'm sure you've heard scales before, so picture someone playing quarter notes:
bum, bum, bum, bum, bum, bum.....etc

But it would sound really wierd if you had this instead:
bum, bum, buu,ubuuum,ubuuum,ubuuumuuuuuuum.....etc

In the second case, the third note the bass player hit is resonating too long and mixing in with the other notes. The poor newb bass player is sitting there wondering why his scales don't sound right, but no matter what he does, that third note just resonates forever. Sadly he doesn't know that it is because of the fingers in his room so he goes out and purchases a new guitar and then a new guitar amp and then some fancy exotic pedals trying to get his scales to sound right - of course this was after months of trying to figure out how to play that third note differently. Sadly, the only way for him to play his scales correctly would be to implement some acoustical treatment and break the fingers of the room so that the room can't hold onto the note. I suppose the other alternative is to break the fingers of the idiot bass player, but let's not go there []

[DrWho]

I've been taught that resistors divorce an amp's damping from the driver, but I don't really understand why that is.

"voltage divider rule". Damping is directly related to the voltage sent back to the amp from the driver - when it goes through a resistor, the voltage drops.

[Coytee]

Ok, so before MY fingers get broken for asking too many questions... do I get some of the following correct?

<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Picking the top graph so were on the same page...

It is a slice of 20hz to 200 hz. The time window is a duration of 400 milliseconds.

During the 400 milliseconds, a snapshot of the sound was taken. Various frequencies were stronger than others (the humps as reading from left to right). Those peak frequencies lasted for various durations of the said 400 ms time frame before they withered away (except perhaps the first one).

On to the next chart... same snapshot I presume but after some room treatments??

Now by virtue of the fingers being shorter duration, that shows us that those notes dont linger as long into the 400ms window. Since they die sooner, they either wont resonate in the room or if they do, the problem is at minimum better than it was before when they had the longer lifespan.

So, if I have the basic above under some reasonable understanding, lets look at one of the fingers on the top chart. There seems to be a clearly noticeable line going down the center of the finger and the slops seem to be sharp. Meaning, if you looked at the fingers as a knife blade they have a sharp edge with the blade underneath.

Can you have a more rounded blade (fatter/thicker) or do they all tend to be thin?

[mas]

Waterfall or Cumulative
Spectral Decay Plots

A cumulative spectral
decay (CSD) plot is a 3-dimensional display that reflects a loudspeaker's frequency
response as well as its phase response. A CSD plot resembles a waterfall and
shows how a loudspeaker acoustic output decays, at each frequency, in response
to a steady-state sinewave input that is suddenly turned off. CSD plots reveal otherwise
hidden enclosure or other resonances and are used to assess loudspeaker
transient response. They are also useful to display resonances in enclosed
spaces. A CSD waterfall is attached.

The
Waterfall is more properly known as the "Cumulative Spectral Decay"
(CSD) plot. This plot technique is generally credited to Fincham and Bernam (of
KEF) who first used it to detect resonances and internal box reflections in
loudspeakers.

A
waterfall is a presentation of both frequency domain and time domain data on a
single graph. Time domain data is voltage or pressure as a function of time,
usually in the form of a measured impulse response (origination from a pulse or
MLS measurement), which covers all time (but can be assumed to decay to
insignificant levels within a finite time). The frequency domain version is the
decomposition of the time domain impulse response into periodic cosine
waveforms via Fourier analysis (the impulse response can be represented as a
summation of an infinite number of cosine waves of different frequencies). In
any combined time-frequency analysis, there are inherent resolution limitations
due to the related (reciprocal) relationship of time (seconds) and frequency
(per second). One cannot, for instance, talk about a frequency at a point in
time -- it is rather meaningless to discuss a periodic wave unless (at the very
least) the time length of that period is considered. Hence, a frequency
component cannot be said to start or stop at a specific time. But a band of
frequencies can be analyzed in terms of its energy within a said time segment.

Contrary to the common
conception of the waterfall plot, the CSD
waterfall does NOT show
frequency response versus time! Sound strange? It really shouldnt if you take
a step back and look at what we are saying here. It shows that
(approximate) frequency content contribution to a total response which occurs
after the (relative) time shown in the time axis. At t=0 on the CSD plot, the
entire frequency response is drawn, as the total response occurs after this
time. At t=1 ms the CSD plot shows the contribution to the frequency response
which occurs after 1 ms but not before 1 ms and so on. But note the
caution previously stated above: frequencies cannot start at a precise time! --
CSDs often show the users technique more than the speakers quality! Also note
that if an echo pulse is included in the time segment selected for the
waterfall plot, the frequency contribution of the echo will be present in the
plot for all times before the echo occurs.

CSD waterfalls are most
often used to detect and display resonant behavior in surfaces and enclosed
spaces, be it a speaker cone, speaker enclosure, or an enclosed room. A
resonance will show up as a long decaying ridge along the time axis, due to the
"ringing" of the resonance over time.

The data shown is VERY
SUSCEPTIBLE to measurement and display conditions. The inherent windowing (looking
at only a portion of the total data) that is involved in the processing is
hacking into the most active part of the impulse response. Results will change depending
on the window shape used, the step size being used for the waterfall graph,
on display resolution, and especially on the low-frequency content (even
below resolution) and phase, etc.

Each individual curve trace
on its own cannot be said to carry much useful information. It is the overall
plot, the assemblage of the individual traces that cumulatively present trends.
It is the ridges, shelves and valleys of the overall resultant surface generated
by the summed individual traces that provides a qualitative, but only slightly
quantitative, measurement. Thus, it is the relational pattern that is valuable.

And as Doc has mentioned,
the ridges indicate the persistence of a particular resonance over a particular
frequency passband. Another way to imagine this is to think of a hand clap. In a
relatively non-reflective space, this impulse would be well defined as the
acoustic energy would decay rapidly in intensity following the clap itself. In a highly reflective space (but not large
enough to reinforce a long delayed path (>60-80 ms) sufficient to allow the
reflection to be heard as a distinct echo), the clap would be experienced to
persist and not be as distinct.

Another example focusing
on the source rather than the enclosure might be to think of a gong. A gong,
once stuck, will persist for a long period of time. And the resonance would be
characterized by a fundamental frequency as well as harmonic multiples of the
fundamental frequency. These resonances would appear as ridges extending from
the (often) x axis, as their intensity and persistence would cause them to be
more greatly distinguished with the passing of time. If, on the other hand, we damped the gong and
then stuck it, the result would be a thunk, and there would be little of no
resonance or persistence in sound shortly after the strike. Thus no significant
ridges would be observed, and the spectral content would decay quickly after
the time 0 intensity.

And while the technical aspects of such diagrams can become a bit dicey, the usefulness of the diagram should be readily apparent. It provides a very readable graphic presentation of a real behavior that is not otherwise easily presented.

And more importantly, the measurement provides an accurate representation of what is other wise a very complex measurement. Even the best room resonance calculators assume the simplest and most ideal rectangular spaces, with all surfaces considered uniform, of the same material with the same reflective coefficients an with NO variation in the dimensions. And once you involve any real room variations, ranging from doors, to stairway alcoves, foyers, etc., you quickly enter into the realm of a very complex relationship of various tuned spaces which sum. And these can have a dramatic influence upon the resonance of a space, rendering the calculator's result worthless - especially as any treatment needs to be rather precise. And even with precise treatment, one is not going to flatten the room response. The best you are going to do with treatment is to decrease the offending peaks by 3 dB - which is a significant achievement - and also a good reason to avoid room dimensions that may place various modes in the same region which may result in their being increased by a maximum of 3dB for each summation. Thus if you have 3 modes superposed in the same region, the potential for a 9dB increase in resonance gain is not going to be easily decreased in a meaningful way if a trap can only decrease it by 3 dB! Thus, this is why we try to spread the resonance mode standing waves out and distribute those peaks about he room.

If anyone is interested in
the technical limitations involved in such measurements, I can dig up a bit
more info. But I am thinking that this
will already have Chloe ready to do some damage control

[DrWho]

Sounds like you've got it - well at least understand it the same way I do [Y] Who knows, I could be entirely wrong []

The "sharpness of the knife" is called the "Q". The Q is some fancy mathematical term derived to have a meaningful way of describing the steepness of frequency related phenomenon. For example, a Q = 1 crossover means that it rolls off at 6dB/octave. The Q of the fingers in the diagram are going to be around Q=10 (which I believe is 60dB/octave, but don't quote me on that). Basically the tip of the knife blade is the "center frequency" and then the Q defines how much the surrounding frequencies are affected. I believe by definition, a Q=0 affects every frequency equally and a Q= infinity affects a single frequency.

But to answer your question: no, they don't have to be thin.

I hesitate saying this, but the Q that you see on the graph is going to change depending on how you window the impulse response. For a basic understanding of what's going on, I think it's ok to trust that the measurement shows a meaningful accurate result. I only mention it because "improper" windowing can yield inaccurate conclusions...so sometimes the graph isn't representative of what's going on. I'll see if I can't generate some waterfalls to illustrate the point. Think of windowing as choosing which magnification to use on your microscope. Low frequencies are huge, so it doesn't make sense to "zoom in" too far. Likewise, high frequencies are small, so you need to "zoom in" more on them...

[mas]

I guess I am a bit confused as to why this graphical representation is so confusing...[]

That is one of the really nice things about them. Assuming you have a good measurement, it makes it easy to identify them by sight. So for now, please don't worry about the window size, etc. etc. etc.

The ridges or fingers that persist are resonances centered at a particular frequency. The longer they protrude, the longer the persistence (in time/duration) of the resonance. The lack of defined ridges indicate little or no resonance as we are referring to it. (As we are not referring to reverberant fields.)

Oh, and the ridges do not have to be narrow! They can be very narrow or much wider. A good example of wider ridges is in a room where several modes have center frequencies near to, but not identical to, each other. They will sum and their width can be rather wide. And these become much more difficult to damp. In fact, this is why the reference to room dimensioning occurs...as dimensions that are multiples of each other do exactly this. And references to 'ideal' room measurements refer to dimensions that will tend to reinforce standing waves where the frequency centers are well spaced, thus minimizing the summation of the energy, making the individual resonances slightly easier to damp.

This reinforcement is also a very common result of several adjoining rooms or a room with alcoves and adjoining spaces. Each space has its own resonant characteristics, and they will combine in some very interesting ways in the 'main' room. The more complex the summed resonance - both in terms of the Q - or width- of the resonance, and the gain, the more difficult it is to address these problems.

If you want to see some nice CSD/waterfall plots, go check out he Alcons ribbon specs I posted over in the ribbon thread. Given the intensity (gain) at which these are measured, the plots look so good they appear doctored!

[WMcD]

I'm not going to discuss the plots with mas. He knows too much. But let me say that I believe true waterfall plots in sonar are different. They move a frequency plot down the screen continuously.

But on the issue of resistors and damping:

We start with the concept that the speaker spring and mass resonate at some frequency, which is pretty much Fs. So it does not want to stop without some damping. The damping is like putting a finger on a tuning fork.

There is some mechanical resistance within the system and this shows up as Qms. This figure is pretty high and shows the mechanical resistance doesn't damp out the resonance very much.

However, the mechanical system is attached to the electical system of the driver. This is the voice coil and magnet. This electrical system works like a motor, generally. The current through the voice coil from the amp make the mechanical system move, and make music. More current, more force, more music.

But, this electical system also works backwards, as a generator. Assume the diphragm is the crank handle on a magneto. The higher the current demand, the harder it is to turn the crank. And the stonger the magneto (bigger magnet, more windings) the more current it can make.

Generally, drivers with lots of windings and big magnets are both good motors and good generators. This shows up in the number called Qes, the Q of the electrical system. This is a low number. The total Q of the system (Qts) is typically close to the Qes.

We're not quite done yet. How hard you have to turn the crank depends on the amount of current possible. (Turning the crank is like a stonger finger pressure on the tuning fork, of course, it damps out the resonance faster.)

We look at our driver as generator and figure out what is limiting current. It is trying to force current through the electrical resistance of the voice coil back into the amplifer output terminals, and any other resistance in the circuit.

Any resistance is limiting current, that is what resistance does!

We have to look at resistance in the loop. The voice coil has a resistance of about 8 ohms. Most speaker wire runs are far less and thus the voice coil his a major contributor.

The only thing left is the output terminals of the amplifier. This is the output impedance of the amp. This is difficult concept because we're not very use to thinking as the output of an amp being a "load" on a generator (the driver). Actually, here the speaker is the source of current at resonance - the real supplier of current.

Amplifier with feedback mechanisms typically have very low output impedance (high damping factor). This is because when there is no input to the amplifier, it will maintain zero volts at the output terminals. This is so even if something (like the resonating speaker) is forcing current through the output terminals. The feedback loop senses that something is trying to drive the output above zero volts and the feedback loop turns on the amp to prevent a voltage difference across the terminals.

If the amp is maintaining zero volts difference at the output terminals, it is acting like a wire, a dead short. There is current flow (high current is equivalent to "hard to turn the crank) but no voltage.

That is not a contradiction. A wire or zero resistance allows max current but no voltage drop.

Maybe we have to go back to resistance in the wire or some dropping resistor or L pad. These do imped the flow of current, making it less. Remember that the the use of "I" for current is for Intensity of current.

If there is less current in the loop, the "damping finger" of the voice coil is less strong. The "Qes" of the overall system (speaker plus wire plus amplifier terminals) goes up.

Gil