Principles: Time of Arrival Delays, vs Phase tuning ?

[john61ct]

Thanks so much for taking the time for such a detailed answer, will over time check out that calculator page (whooosh!)

If anyone can suggest more ELI5-level explanations written for noob laypeople, would be much appreciated!

phase when expressed as delay is frequency dependent

Doesn't that contradict what I quoted in the previos post?

> Phase is frequency dependent, the delay will vary. "latency / distance" delays are a fixed delay for the whole signal, not frequency dependent.

OK that's a useful distinction.

How does "group delay" figure in there?

...

> 180 degrees out of phase means full cancellation.

OK, but what does "full cancellation" mean?

> For two drivers in one speaker, as you can see 0.25ms delay can be a problem.

"as you can see" is flattering me there.

> If you are running your woofer and tweeter on separate clocks it's going to sound insane. Even two clocks for two separate loudspeakers is likely to cause problems.

Why would a delay between drivers within a multi-way enclosure have any different effect than between separate boxen, if all are managed by the same active multichannel DSP?

Not my use case, but just to help me understand the principles...

 

[levimax]

If you want to go down the DIY DSP crossover path, which I highly recomend as it is interesting and fun, there is a hard learning curve. Trying to do it without a PC and without a single multi-channel interface is extremely difficult requiring multiple hacks and work arounds. The more you learn the more you will understand why. I would start with getting those 2 pieces and from there you can do pretty much anything with free software. In any case enjoy.

 

[kemmler3D]

On DAC drift its typically <5ppm, so no idea where you conclude that the time drift between 2 DAC >0.25 msec over a few minutes

I also used to think this was a negligible thing, but I was shown results to the contrary in a thread ages ago... unfortunately can't remember where. I am sure it varies depending on the hardware...

Rotating the phase of a signal doesn’t introduce any delay at all. A signal leaving the amplifier with 60 or 90 degree phase, leaves at the same time, but its starting phase is different.

OK, thanks, I think this makes sense... I do get somewhat confused about phase when thinking about complex waveforms and recordings...

 

[kemmler3D]

Doesn't that contradict what I quoted in the previos post?

Not quite - sometimes people will talk about phase and delay interchangably (confusing) because a phase rotation is equivalent to delaying the waveform by that amount of time at a given frequency.

Basically think of a sine wave, one full cycle = 360 degrees of phase (or 2pi radians.) A picture is worth a thousand words here:

How does "group delay" figure in there?

I may mess up this definition, but group delay is like phase shift except there actually is true delay, not just a phase rotation. Often it's a problem in the bass frequencies where bass might be "late" by a full cycle or two.

OK, but what does "full cancellation" mean?

As in the graph above, if you superimpose two waves at the same frequency and they're 180 degrees out of phase, the + and - waves zero each other out, so you get silence.

This is why if you have the delay between drivers changing by even 0.25ms in use, you might end up with as much as (the equivalent of) 180-degree phase shift. Two drivers cancelling each other out is not (usually) what you want, so you can see how that would be an issue.

Why would a delay between drivers within a multi-way enclosure have any different effect than between separate boxen, if all are managed by the same active multichannel DSP?

Same principles at work, but since the drivers in a box are closer together, and since you are counting on them on producing a coherent sound, problems become noticeable with smaller unintended delays.

When two speakers are spaced by 1-2+ meters, and they're (say 2-3m away from you) a delay of 0.25ms becomes much less problematic, because it takes sound roughly 3ms to move 1m.

 

[levimax]

Thanks so much for taking the time for such a detailed answer, will over time check out that calculator page (whooosh!)

If anyone can suggest more ELI5-level explanations written for noob laypeople, would be much appreciated!




Doesn't that contradict what I quoted in the previos post?

> Phase is frequency dependent, the delay will vary. "latency / distance" delays are a fixed delay for the whole signal, not frequency dependent.

OK that's a useful distinction.

How does "group delay" figure in there?

...

> 180 degrees out of phase means full cancellation.

OK, but what does "full cancellation" mean?

> For two drivers in one speaker, as you can see 0.25ms delay can be a problem.

"as you can see" is flattering me there.

> If you are running your woofer and tweeter on separate clocks it's going to sound insane. Even two clocks for two separate loudspeakers is likely to cause problems.

Why would a delay between drivers within a multi-way enclosure have any different effect than between separate boxen, if all are managed by the same active multichannel DSP?

Not my use case, but just to help me understand the principles...

For in and out of phase try this 5 min video.... was helpful for me.

 

[rjp]

I'll give it a try in layman's terms. Phase and time delay are closely related but different.

Phase describes the position (or fraction of the cycle) within a periodic waveform (typically a sinusoid). Phase tells us *where* we are in a cycle, but it does not tell us *which* cycle we are in. Time delay is simply the total elapsed time from the start of a waveform without regard to how many cycles have passed.

Phase and time delay are related through frequency. If we know the frequency and the time delay, we can calculate exactly how many cycles have elapsed. This means we can know the phase (position) we end up at in the last partial cycle. So in a sense, phase can be thought of as modular time.

This is for a single frequency. For multiple frequency waveforms (all music) it gets more complicated. We can easily apply a constant time delay to a wide band signal, and as a result, each constituent frequency in the signal will experience a different phase shift proportional to its frequency. The higher the frequency, the greater the phase shift. This is called linear phase.

It is much more difficult (though still possible) to apply a constant phase shift to a wide band signal, and this is probably something you don't need to even think about in home audio processing.

Time delay and phase delay can be used almost interchangeably when talking about single-frequency signals, and that is where some confusion comes from. If we apply a time delay of 10 ms, and that just happens to be the time it takes for a particular tone to advance by 25% of its cycle, then we have just introduced a 90 degree phase shift (25 % of 360 deg). If we delay the same tone by 20 ms we will introduce a 180 deg phase shift, and so on. The problem is, once we delay this tone by 40 ms, the phase shift is now 360 deg (a full cycle) and it starts all over again at 0. So if we say the phase is 0, do we mean 0 in this cycle, or in the previous one? There is now an ambiguity.

This means that if we have 2 of these tones, a copy with no time delay and another copy with 40ms time delay, they will arrive with the exact same phase (a.k.a. in-phase), but at different times.

I hope that helps make it a little clearer.

 

[Keith_W]

OK this is the relationship between delay and phase. I'll keep it very simple.

Here are two sine waves starting at the same time. The second sine wave (green) is has inverted polarity compared to the first. If you sum the two sine waves, the result is a flat line (pink).

Now we delay the green sine wave by 1/4 period. 1/4 period = 90 deg.

If we delay the green sine wave by 1/2 a period (180deg) the two sine waves are now in-phase. The sum equals double the amplitude of each individual sine wave.

If I remove the summed sine wave for clarity, you can see that the green sine wave is a full 1/2 period delayed compared to the red sine wave. In other words, the impulse is not aligned, but the phase is aligned.

I am sure you can guess what will happen if we delay it by 3/4 period and 4/4 period.

 

[john61ct]

Thank you.

So if this is like the red wave is front left main, and the green is the sub under it, around the overlapping crossover frequency?

Let's say at 80Hz

What are the acoustic consequences for each of those examples? With a music signal not just a sine wave. Does it manifest as delay?

How far off from perfect can be left alone, when is correction required.

I don't want to waste resources making the graphs pretty...

 

[rjp]

With a music signal not just a sine wave. Does it manifest as delay?

How far off from perfect can be left alone, when is correction required.

Once we are talking about a music signal, it's probably best to forget about phase all together. There is nothing you can do about it anyway.
Yes, it manifests as delay, and this time delay is what you adjust.

It seems a little confusing because phase (and phase rate of change , a.k.a. group delay) are often discussed within alignment tools such as REW, but the only "knob" you really have at your disposal is time delay. Well, there is also the phase setting (0/180) for the sub, but this is really just an option to invert the signal.

In you example, you would add time delay to main channel so that it arrives at your ears at the same time as the sub, but this is not as easy as it sounds. The metric used is typically good phase alignment at the crossover frequency, or less commonly, good correlation of the respective impulse responses. But there are many other frequencies involved as well, so no one rule gives the "perfect" number of ms delay. Sometimes you just have to tweak it so it sounds best.

 

[kemmler3D]

Thank you.

So if this is like the red wave is front left main, and the green is the sub under it, around the overlapping crossover frequency?

Let's say at 80Hz

What are the acoustic consequences for each of those examples? With a music signal not just a sine wave. Does it manifest as delay?

How far off from perfect can be left alone, when is correction required.

I don't want to waste resources making the graphs pretty...

So, the consequences in terms of phase are exactly as shown in that image regardless of frequency.

In terms of delay (say 2ms) that is equivalent to a certain phase rotation at 80hz (use the calculator) - because the wavelength at 80hz is pretty big, a little delay doesn't put it as far out of phase.

Think of phase as a percentage of the wave, and delay as an absolute amount of shift. Low frequency waveforms are very long so delay doesn't cause as much phase shift and is less problematic.

 

[Keith_W]

So if this is like the red wave is front left main, and the green is the sub under it, around the overlapping crossover frequency?
Let's say at 80Hz
What are the acoustic consequences for each of those examples? With a music signal not just a sine wave. Does it manifest as delay?

OK so let's say red = main, green = sub, and 80Hz is the XO frequency.

The acoustic consequence is cancellation or reinforcement at the XO frequency depending on the phase alignment of mains and sub.

Music may have phase all over the place depending on what kind of recording it is. Electronic music - probably not. Acoustic recordings - definitely yes. But the point is, music does not know where the XO point is. If there is cancellation at that frequency, you will have a hole in your freq response. If there is reinforcement, you will get a bump in your frequency response.

How far off from perfect can be left alone, when is correction required.
I don't want to waste resources making the graphs pretty...

As you can see from aligning phase, it may cause the impulse response of the mains and subs to drift apart, since your only control is delay*. Therefore you have two questions to ask yourself. Should you prioritize:

1. Impulse alignment? How far apart can the impulses of main speakers and subs be misaligned before the delay becomes audible?
2. Phase alignment? If phase is well aligned, there is less cancellation and therefore a flatter frequency response. You get better timbral accuracy.

The overwhelming consensus is that timbral accuracy is more important, therefore phase alignment is more important. Of course, we don't want huge delays between subs and mains either, because at some point that becomes audible (e.g. if it is misaligned by 10 seconds, you would surely hear that). The audibility threshold is unknown**, but it is thought to be 1 period of the frequency in question. Maybe more. So for a 100Hz XO point, the threshold is about 10ms.

* Strictly speaking this is not true, you can also have things like all-pass filters and FIR to nudge the phase into alignment without having to shift the impulse response too much, but that is a very advanced discussion. Put that out of your mind for now or file it away for something you can look at in the future - I only mention it for ASR pedants.

** see research on group delay audibility thresholds - Liski, Makivirta, et al. Those studies were done with headphones and test signals, and the lowest freqs tested were 200Hz from memory. So the number I gave is a pure guess based on extrapolation.

 

[mdsimon2]

I made some measurements of what happens to crossover frequency response when using two independently clocked DACs which may be helpful -> https://www.audiosciencereview.com/forum/index.php?threads/vb-matrix.48989/post-1756250.

Michael

 

[john61ct]

Once we are talking about a music signal, it's probably best to forget about phase all together. There is nothing you can do about it anyway.
Yes, it manifests as delay, and this time delay is what you adjust.

It seems a little confusing because phase (and phase rate of change , a.k.a. group delay) are often discussed within alignment tools such as REW, but the only "knob" you really have at your disposal is time delay.

Are these assertions only within what REW offers? Or adding Rephase, or going to say Acourate to get FIR filters?

I am constantly coming across references to using FIR to "linearize" crossovers, as functionally equivalent to creating linear phase crossovers using FIR from scratch.

The only downsides presented being DSP power needed at LFs and resulting latency delays from that processing.

 

[john61ct]

Fantastic response thanks much.

Will be a while absorbing all that.

...

you can also have things like all-pass filters and FIR to nudge the phase into alignment without having to shift the impulse response too much, but that is a very advanced discussion. Put that out of your mind for now or file it away for something you can look at in the future

But aren't FIR and all-pass filters routinely used in common DSP tools? A noob like me might just start with the more automated ones...

Or are you putting me off using those tools within this "speaker building functions only" context specifically crossover-related phase tuning ?

I did say setting DRC and MSO aside...

 

[Keith_W]

But aren't FIR and all-pass filters routinely used in common DSP tools? A noob like me might just start with the more automated ones...
Or are you putting me off using those tools within this "speaker building functions only" context specifically crossover-related phase tuning ?

I am not trying to put you off anything. I encourage you to go with more manual design, since you seem to be curious about how things work. But let's be realistic here, this is only something you attempt after you have generated your first filter and you understand what you are doing. You have more important things to worry about, such as how to take proper measurements, especially proper timing measurements. There is a lot to learn, and I don't want to overwhelm you. For now, all you need to know is that it's another possible tool you could use. You don't need to know in detail how to use it. But if you DO want to know, it's all there in my Acourate guide. Same link as the REW eBook in my sig.

 

[john61ct]

I appreciate that, but "overwhelm" in one topic area just leads me to divert to others, come back later.

My brain does not work typically, and the hands-on will always lag far behind my attempts to grok the theory.

Plus my budget restrictions, keep my eyes open for great value used gear, but REALLY want to be sure, even for what most would call small investments.

I do greatly appreciate your contributions to the community, and my own learning curve.

 

[sigbergaudio]

@john61ct The details and complexity of the answers you are getting, seen against how much of it you seem to be able to grasp currently, combined with the fact that you don't have a working PC to start testing any of this, leaves me wondering if we are shooting sparrows with cannons (Norwegian saying implying that we are using a lot more energy than we need and/or are trying to solve a small problem with a very complex solution).

So I thought I'd ask if understanding all of this is an independent goal regardless of your project, or if it's only a goal if it is relevant to your project?

If the latter, I think it would be helpful if you could explain a bit more what you are attempting to build, and for what purpose, so that we can evaluate if understanding (or even caring) about the details of this topic matters to you at all. One of your answers implied it was a mobile setup, and seemed to imply that there would be multiple listeners, while a few posts earlier you implied that 95% of the time there would only be one main listening position, which is contradictory.

So it's still unclear to me what you want to build and what the use case is.

 

[sigbergaudio]

> I believe you if you say so. I got this off AI - so it may well be nonsense

...

I appreciate your transparency, but please abstain from posting "facts" gleaned from AI sources here.

Very unreliable, and in any case such delay sources (analog only components) are OT in this thread as I stated.

Something quite fun and ironic, is that AI often use forums like this one to find answers. And on forums like this one, it's very popular to answer questions despite not actually knowing the answers. So then AI ends up with the wrong (or at the very least imprecise) information too, and then people post that to the forums again after asking the AI, and around we go.

 

[john61ct]

Another instance of Dr @Floyd Toole 's Circle of Confusion

 

[john61ct]

understanding all of this is an independent goal regardless of your project, or if it's a goal if it is relevant to your project?

My learning is more the point, the project(s) just provide a challenging context.

Providing "all the details" of my evolving goals and plans would I think be a diversion in this type of theoretical / academic thread, for a broader background I've been more forthcoming in more practically-focused other threads I've started.

However I am very appreciative of anyone's interest in responding, so I'm happy to answer specific questions as they arise.

Yes the system will move between different spaces, mostly off grid and including outdoors. Some of the larger, AC grid-powered components may need to stay back at my S&B house, aka home at least of my teen kids.

Dance parties and group film watching do occasionally happen, but usually it's just me, 90% music - both critical listening, and sometimes just background.

The goal is to focus on Stereo, prefer to preserve the possibility of acoustic envelopment

with upmixed multi-channel available. So source channels starting at 5, maybe seven in future, sourced from analog lines.

Several channels serviced by "a stack" to get FR, smaller (passive multi-way) mains + trueSubs, MBM Coupler boxen on the F-L/R stack in between, likely DIY.

Also freely placed mono trueSubs if needed.

Ideally no box bigger than 12x12" face, up to maybe 15" deep, although for the S&B house maybe a pair of BRuTeS (Bone Rattling fUll-size TruE Sub).

The mono trueSub collection, no matter on which channel, may all be separately managed by @andyc56 's MSO - but if I understand correctly, that's not involved in these "speaker building" aspects of DSP.

I will want to be able to switch between such factors, general DRC, "smoothing for multiple LPs" etc as opposed to the "ultimate pinpoint" coherence / soundstage and transients performance

even if that cannot be done by flicking a few switches, keep all the wiring readily accessible.

Of course if I am unable to accrue envelopment advantages or other SQ benefits from the mostly-stereo approach - each step validated by testing - then I will settle on one stable configuration I determine is "the best" compromise.