Reading and interpretting various graphs correctly! Unconfuse me! =)

[wigginjs]

I doubt I'm the only person who falls into this category. I've been reading and studying about speakers for a few years now, but I feel like I've yet to find a definitive source for an answer to the following questions:

What is the correct way to read and interpret graph x, where x =

Frequency Response (frequency vs. amplitude)
Phase Response (frequency vs phase)
Impedance (frequency vs resistance)
Impedance Phase (frequency vs phase)
Group Delay (frequency vs time)
Cumulative Spectral Decay (frequency vs amplitude vs time)
Step response (amplitude? vs time)
impulse response (amplitude? vs time)


Some of these I'm actually quite familiar with. Lets take frequency response for example. I have an understanding of what an ideal graph would be (flat from 1Hz to infinite Hz). I know how to interpret what the effect of variations from the ideal graph would be. For instance, the graph is flat to 20KHz, but rolls off at 24db/oct starting at 200Hz, I know that there would be poor bass response and I can imagine what that sounds like. But for the other graphs listed I'm not quite so certain. What are the "ideals" for those graphs? What are common variations and what is the effect of them? Perhaps some of these graphs don't have "ideals" per say? I realize this is a very broad question, but it seems like measurement graphs are one of the most important things for a speaker builder to understand. I think I am also right in my assessment that the majority of people involved in DIY audio do not have a COMPLETE understanding of how to get the most out of these graphs. Thanks for your help and I will chime in tidbits of information as I find them. My hope is that this thread can be a solid reference to newbs or seasoned veterans who have small knowledge gaps.

[SY]

You could write a book about that. In fact several people have. I'd start with Joe d'Appolito's book on speaker measurement, which will disabuse anyone of the notion that frequency response is a simple curve.

I'd also look at Floyd Toole's papers and presentations at Harmon International's website. Sig Linkwitz's site is full of good info on correlating measurements to sound and is a must-read. There's lots more...

[Svante]

Originally posted by m0tion

Frequency Response (frequency vs. amplitude)

Probably the most useful of them all. As you say, it is clearly visible if there for example is poor bass.

Originally posted by m0tion

Phase Response (frequency vs phase)

In itself, it has rather a small impact on the perception of the sound. However, if there are multiple drivers involved (woofer-tweeter) the phase relation is very important since it will determine how the sound adds up around the crossover frequency.

Originally posted by m0tion

Impedance (frequency vs resistance)

Well, really frequency vs impedance. Impedance has a resistive and reactive (inductive or capacitive) part. This graph is useful in crossover design, or to determine how difficult a load a loudspeaker is for the amplifier.

Originally posted by m0tion

Impedance Phase (frequency vs phase)

Complementary info to the impedance curve. The phase shows the relation between the resistive and reactive parts of the impedance.

Originally posted by m0tion

Group Delay (frequency vs time)

IMO one of the most overrated graphs.

Originally posted by m0tion

Cumulative Spectral Decay (frequency vs amplitude vs time)

This is also an overrated graph IMO. Typically, everything that can be seen in the CSD can be seen in the frequency response.

Originally posted by m0tion

Step response (amplitude? vs time)

Yes amplitude, which in turn can be for example sound pressure or voltage.

Useful for the engineer during design, but hoplessly useless for the consumer. If one is not familiar with the restrictions it can very easily mislead the user. For example, an allpass filter has a terrible step response, still the allpass filter has almost no audible effect on the sound.

Originally posted by m0tion

impulse response (amplitude? vs time)

Same as step response. However, impulse response is often used as a step to get the frequency response and for this it is good. The Fourier transform of the impulse response gives the frequency response.

[wigginjs]

In itself, it has rather a small impact on the perception of the sound. However, if there are multiple drivers involved (woofer-tweeter) the phase relation is very important since it will determine how the sound adds up around the crossover frequency.

So, what would the "ideal" phase response look like? I would imagine that because each driver's position is fixed with respect to the listening position that it would not be possible to have a flat phase response due to the fact that wave length changes based on frequency (unless it is possible to correct for this with digital filtering somehow). Would a flat phase response even be optimal or is it only important for the phase response to be linear? Is phase response in and of itself even important or is it simply the fact that if you have multiple drivers they need to be in-phase at their crossover points in order to avoid dips in the frequency response?

I think one reason that the phase response graph is difficult to read and interpret is that it "wraps" (or it seems to at least).

[SY]

Measured where, in what environment, and how? What reference point for arrival time corrections?

You're thinking of this the way you would an amplifier- put something in, measure what comes out. The problem is that a speaker is a 3 dimensional object that radiates unevenly into a reverberant 3 dimensional space. And the nature of that unevenness profoundly influences the way it sounds to the ear.

Making it worse, there's no consensus on what the desired unevenness of polar pattern with frequency should look like. As an example, a dipole, point source, and omni will all sound profoundly different even if their on-axis 1 meter responses are the same.

[wigginjs]

SY:

It seems to me that for frequency response, phase response, and CSD the most typical measurements are performed in an anechoic (or semi-anechoic, gated or some such) environment on-axis (whatever that means, truly on axis is it is a single driver, acoustic center if it is multi driver?).

I'm not sure what you mean by "reference point for arrival time corrections". I don't think that for the purpose of loudspeaker evaluation the absolute phase is important in the least. It's simply the relative phase of the measured samples taken. Since the intent of a phase response graph is not to measure SPL I don't think it would matter how far away your measurement microphone is from the loudspeaker.

In this environment the polar pattern shouldn't make a difference should it? I recognize that no one's real life listening room is an anechoic chamber, but I don't think that makes the measurements any less valid.

Do these assumptions make this question more approachable?

[SY]

Anechoic measurements are great if you're going to use the speaker in an anechoic chamber. But at minimum, you need to know anechoic frequency response as a function of horizontal and vertical angle, and how that varies with power level and thermal history. This doesn't get you in-room bass response, but it's a start. Interpretation is a challenge and, as I mentioned, there is no universally-accepted standard for what's "good." You can only say, "Does it hit the target?"

Time-of-arrival is simple as long as all sources are coincident. Unless you're measuring from quite far away, they're not. That introduces some interesting non-minimum phase complications which won't show up if you use a simple Hilbert transform on the magnitude data.

[Tom Danley]

Hi mOtion
You ask;
“So, what would the "ideal" phase response look like? I would imagine that because each driver's position is fixed with respect to the listening position that it would not be possible to have a flat phase response due to the fact that wave length changes based on frequency (unless it is possible to correct for this with digital filtering somehow). Would a flat phase response even be optimal or is it only important for the phase response to be linear? Is phase response in and of itself even important or is it simply the fact that if you have multiple drivers they need to be in-phase at their crossover points in order to avoid dips in the frequency response?”

Well, if your idea of a perfect loudspeaker is one, which changes nothing about the signal instead of being time dispersive as is normally the case, then the answer is easy.
A perfect acoustic phase response is one which is zero degrees or 180 degrees in an inverting system. That phase angle combined with flat amplitude response results in the sound coming out having the same waveshape as the electrical signal going in.

To be clear, this has nothing to do with phase rotation as a result of delays like how far the mic is, this is the acoustic pressure’s phase angle compared to the electrical signal, once ALL those fixed delays have been removed. Those fixed delays do not change the waveshape as they affect all frequencies equally.

In reality, even a single loudspeaker driver does not usually have “zero degrees” of acoustic phase at least in the bottom half of there range so the problem is much larger than simply aligning the driver up in time. Even one driver usually appears to wander around in time.
Also, in time, the origin of most drivers is some equivalent distance behind the radiator and woofers can even be “feet” behind in time.
Richard Heyser developed a measurement system to quantify this and wrote a number of papers on this subject, which may be of interest.
His work is timely too as many measurement systems have large errors when they present a “phase plot”

Loudspeakers which preserve phase (input waveshape) tend to be types who’s conversion mechanism is not current accelerating a mass like an electrostatic speaker or highly loaded horn and the Manger, these also tend to be a “one way” speakers to avoid the phase shift spanning each crossover point (except for first order).
With DSP, one has filters which have linear phase can be used, leaving the raw drivers phase responses.
Multiway speakers can be partly corrected with DSP too, at least for one single location in space but since the individual drivers are too far apart to add fully coherently (less than ¼ wl apart), this is not a global fix, but is good in one spot.
We sell commercial speakers at work which are multi-way horns which also preserve waveshape and act / measure / sound as if they were a single driver, although too large for home use. They work because the drivers are less than ¼ wl apart at each crossover junction and so add equally in all directions without reflections.
Lastly, Time may not the best way of seeing some of this stuff, what is better is something related to wavelength or the acoustic size of whatever.
For example two perfect high pass filters or speakers, one with a cutoff at 10Hz and the other at 50Hz.
One see’s that the 10Hz filter has WAY more group delay and it would be normal to think “this is bad”. In reality, it is the correct amount for that filter at that frequency, follow me? Because it is 10Hz, everything is 5 times longer (in time) than at 50Hz.
Maybe a better to see it, another way of looking called “Wavelets”.

http://users.rowan.edu/~polikar/WAVELETS/WTpart1.html
Best,

Tom Danley