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Discussion Starter · #1 ·
I thought I'd start a thread about crossovers, EQ and other filters affect the output and how it interact with the acoustic output of the system.

I mostly use MiniDSP nowadays, they are cheap and offers great versatility. For this setup I've simply put the unit between the I/O of my soundcard.

I will use three terms here; Magnitude Response (MR) - Phase Response (PR) - Group Delay (GD). The group delay is a derivative from the frequency response (Mag+Ph). The negative slope of the phase response will give a peak in the group delay. A negative slope in the phase response equals delay of the signal. Pure time delay will look like a flat downwards sloping line in the phase response viewed in linear mode.

Let's begin with crossovers. Here's the magnitude response of 1st, 2nd, 3rd, 4th and 8th order Butterworth (BW) filters with a lowpass frequency of 100Hz.



Here is the phase response for the same crossovers.



Notice the slope of the BW 48dB/oct filter, and check the GD plot here.



As seen here, the LR48 lowpass introduce almost 6ms of delay centered around 100Hz. This can be an issue, but it can also be useful...


Here is MR, PR, GD of Linkwitz-Riley crossovers;



Linkwitz-Riley (LR) got a smoother transition than Butterworth (lower Q). LR filters will always be even order, i.e 12-24-48dB/oct.





By looking at the PR and GD plots we see that a LR48 filter got less delay than the BW filter of the same slope. This is a direct result of a low Q filter.

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Here's some comparisons between Butterworth and Linkwitz-Riley.









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In a minimum phase system, the magnitude response and the phase response are highly related to eachother, a peak or dip in the magnitude response will have an effect of the phase response as well as seen below:





The phase shift of using EQ in a minimum phase system is a wanted effect when correcting for room deviations in the FR. A cut in the magnitude response will become a negative delay at that frequency. This is really important!

Why is it important? Look here;





What do you think happens when you introduce a EQ cut at ~42Hz to make that response flat...?


More tomorrow...
 

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Cutting 42hz will lower its amplitude, a shorter peak in amplitude means it's takes LESS time to reach the peak resulting in less GD or delay at the frequency


Hanatsu, awesome thread can't wait to see where it goes.
I've been wanting to make a thread like this for a while, I'm just not as smart as you on this stuff your better to do it . Again can't wait to see more :)
 

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Yep so it will drop group delay at 42 hz, in this case it may also have a favorable impact on phase? While this may be easier to demonstrate and see at low frequencies isn't it also perceived less at these frequencies? How do you know when you need to intentionally influence group delay or phase?

Also is all the bouncing around on the 48db slopes due to needing two filters in mini DSP to achieve this slope and some sort of interaction between the two? Or would you see the same crazyness from any other DSP that can do 48db slopes (I can't think of one off top of my head)?
 

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Discussion Starter · #4 ·
You are both right. Group delay will indeed be lowered. Since GD is derived from phase, it will certainly have a favorable impact on phase (in a minimum phase region).

Let's continue using this measurement as an example.





Now let's make a correction filter using a normal parametric equalizer.





...and here's is the result!



In the first example we had a phase shift of 190deg between 20-100Hz, in the EQed response the phase shift is now 165deg, addition to this the response looks much flatter (unfortunately I didn't use the same scaling of the phase plot in the measurements above).

The resulting group delay looks like this;



The EQed response got a group delay of 35ms in a fairly smooth transition. The subwoofer system without EQ got a group delay in the same range of about 40ms and wild swings in the same region. Equalization in this region lowered the delay of the system by ~5ms in total. Between 30-100Hz the effect are even greater, from 28ms to 14ms. That's half the delay.

Understand how this relates to, let's say vented subwoofers?

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Another thing that has been discussed lately is Allpass Filters (APF). An AP filter can alter phase without affecting the magnitude response. An APF is used if you want to alter phase in a frequency specific range. Not all DSPs allow you to create an APF but the MiniDSP can do it by creating a biquad.

This is how an allpass filter work. Notice its MR and PR and the resulting GD.








Here we introduced group delay without affecting the magnitude response (flat as you can see). An allpass filter can be used if you want to add frequency dependent delay and not the entire signal as with time delay.


A perfectly time coherent system would look like this:



Zero delay at all frequencies... So what if we could do better? Get closer to that perfectly time coherent system. What if we could make an arbitrary phase response independent of the magnitude response? What use could this have and what is required to do this?



More tomorrow... ;)
 

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Well I'm fairly certain you're leading up to FIR filters in order to fix the group delay in the 40-120hz range somehow. Can't wait to learn more!
 

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Discussion Starter · #9 ·
Yes. We're heading towards FIR processing. In the next part we gonna explore what FIR based processing is, what it can do and what a FIR based DSP does to the signal. First off, let's be done with our previous example and see what an arbitrary phase response can do to the time coherency of the subwoofer in question.





Notice the upward sloping phase response compared to the other measurement where normal EQ had been used.

What we can see here is an almost flat group delay. This is not possible with the use of normal (digital IIR) processing. The way we attain this is through an arbitrary phase response not dependent of the systems magnitude response.

We shall go through this in detail next time... a little shorter post this time to make up for the next one ;)
 

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So.
Let's just say you didn't have REW ( not saying I don't or don't know how to use it)
Just hypothesize with me here,
If someone used there IIR deq to tune there system and in rephase set the phase eq to the same centers as your deq but set the phase eq to the opposite of what the deq is set, would that align the phase responce in a basic way? Just for eq not for xo

Thanks,
Cheers
 

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Discussion Starter · #11 ·
So.
Let's just say you didn't have REW ( not saying I don't or don't know how to use it)
Just hypothesize with me here,
If someone used there IIR deq to tune there system and in rephase set the phase eq to the same centers as your deq but set the phase eq to the opposite of what the deq is set, would that align the phase responce in a basic way? Just for eq not for xo

Thanks,
Cheers

That's an interesting question. One that got interesting explaination. I will cover this in the next part ;)


Sent from my iPhone 6 using Tapatalk.
 

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While I am thoroughly impressed that all this can be done with a DSP alone, audibly how will this sound different than simply EQ'ing for frequency response. What are the audible benefits to getting my group delay and phase basically flat? While interesting in theory, I don't understand why I care yet.
 

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While I am thoroughly impressed that all this can be done with a DSP alone, audibly how will this sound different than simply EQ'ing for frequency response. What are the audible benefits to getting my group delay and phase basically flat? While interesting in theory, I don't understand why I care yet.
So,

If you flatten your responce with issues in phase against drivers, your not hearing it the way it should be. It is possible to have a flat responce but have it sound bad or colored because of the phase.

Analogy (using made up numbers)

If you have two speakers one in each door, the frequencies that they play are about the exact width of the car , The one on the right the wavelength travels through the air about 3 feet before it get to your ear. Let's use 300hz for example, and let's say 300hz is 3' long. The speaker on right when playing 300hz hits your ear exactly at the peak of the wave form. The speaker on the left is 1.5feet. Now 300hz is only halfway to its peak when it hits your left ear. Half way is 180° being that 3 feet would be 360° . 180° means it's out of phase with the other side . Now let's look at 600 Hz Let's say it's 1.5' long it's in phase for the left ear , and 180° out of phase for the right here . Now let's look at every frequency between 300 and 600 Hz. As frequency increases the difference in phase between the two drivers Slowly starts to come back in phase with each other midpoint and then slowly starts to become out of phase with each other by the time we get to six an slowly starts to come back in phase with each other midpoint and then slowly starts to become out of phase with each other by the time we get to 600. Now think of it swinging back-and-forth from side to side in and out of phase all the way through the spectrum up to about 1K


Wouldn't it be nice to correct all of those anomalies? It would make your flat frequency response sound a whole lot better and make it more dynamic there would be minimal need for time alignment in areas where it is minimum phase or frequencies that are at or longer than The distance between you and the Speakers .
 

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While I am thoroughly impressed that all this can be done with a DSP alone, audibly how will this sound different than simply EQ'ing for frequency response. What are the audible benefits to getting my group delay and phase basically flat? While interesting in theory, I don't understand why I care yet.
Check out these links, I think I am finally gaining a tenuous grasp on phase. I have been doing a fair amount of reading.

Linear Phase vs. Minimum Phase EQ

https://www.youtube.com/watch?v=efKabAQQsPQ

http://archimago.blogspot.com/2015/04/internet-blind-test-linear-vs-minimum.html

Oops, actually linked the same thing twice, but now its fixed.
 

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Check out these links, I think I am finally gaining a tenuous grasp on phase. I have been doing a fair amount of reading.

Linear Phase vs. Minimum Phase EQ

EQ: Linear Phase vs Minimum Phase | The Audio Spotlight

https://www.youtube.com/watch?v=efKabAQQsPQ
Good links,
However we are using these tools so very differently than the reasons shown in the videos.

Although mastering has its uses for shaping a track or its sounds within the tracks. We use it strictly for timing. Immagine a TA control for frequency instead of distance. For some frequencies timing the frequency would eliminate the need to time over distance. Even though they are one in the same (frequency =distance) It's just a different way to look at it .

If you delay a speaker it fixes only one frequency. But messes up others. The more of less you change your TA controls it makes one frequency line up, while others are not lined up. Now think of a TA control that adjusts for frequency wavelength at all frequencies.

I know It's not that simple, the tools are complex and difficult to use. But its promising
 

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The important thing is to stay away from loud concert speakers and such, and hope to have good genes in the ear department so you can enjoy the benefits of such accuracy.
:)
 

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Discussion Starter · #19 · (Edited)
Ok, let's continue. I feel I must address this question first...

Why should we care about the delay corrections in low frequencies?

This is highly related to how we perceive group delay, how we perceive phase. First off, let's break this down to three different types of phase audibility;

1. Absolute Phase... which I dare to say is completely inaudible.

2. Relative Phase between multiple speakers. This is highly audible, it relates to the way we perceive localization in the ITD range of our hearing (lower frequencies). Phase localization is very prominent from the modal region to about 1kHz, where it starts to diminish, beyond this point we rely less and less on phase for localization. We can hear the effects phase have on the magnitude response much higher than that, cancellations are basically different sources of sound being close to 180deg out of phase with eachother. Even phantom sources such as reflections got individual magnitude and phase responses, when these interact with the direct sound and cause nulls we get non-minimum phase areas that can't be EQed. Both the transfer function of a room or a car can be referred to as mixed-phase. Some areas are minimum phase, others are not.

3. Group Delay. This is an effect that will be audible at some point, guaranteed. "Group Delay Distortions in Electroacoustical Systems" from 1978 is one of the more referenced study that contains research on this very subject. They found for example that a GD of 3,2ms at 500hz (1,6 period), 1ms at 2kHz (2 periods) and 2ms at 8kHz (16 periods) was the audible threshold at those specific frequencies.

Looking at the numbers one could assume that it's related to sensitivity of our hearing and/or the fact that the audibility seem to increase as we go down in frequency (if we look at the actual period count). It's a well known fact that out perception of phase differences increase in lower frequencies (point nr.2) but once we hit the lowest frequencies results seem to get unpredictable. Anyone that been around the various audio site on the web have heard about the "slow bass phenomenon" at some point, perhaps even experienced it yourself? Is this related to inherent group delay, ringing in the time domain or simply bad equalization? The problem is real, anyone that tuned a car that tried to integrate mids to subwoofers have most likely run into this issue and found that it sounds a lot better after equalization and level matching. Anyone that have built different types of enclosures knows that they sound somewhat different, I believe the difference largely lies in the phase response (if we EQ responses to the same using "normal" IIR filters.)

Here's a little tidbit; About two years ago me and a friend made an A/B/X blind test of different forms of distortions in loudspeakers by adding filters to the signal. Our results of this test were both interesting and inconclusive. We found that music that had a lot of harmonics added to the baseline fundamental had a lower audibility threshold. We also both preferred a vented bass over the sealed enclosure (vent sealed). Theoretically the vented enclosure would be worse, since the port add delay. This would suggest that it wasn't the group delay that caused our preference but other parameters like non-linear distortion. The thing is that we added harmonic distortion electronically to the vented box, yet we both thought it sounded better (I don't this electronic HD filter was fully representative of the total non-linear distortion created in a speaker, therefore it didn't have the effect we thought it would have)

Non-linear distortion adds sound not present in the original signal and logic would suggest that this distortion would occur simultaneously with the fundamental (correct me if I'm wrong here). The non-linear distortion will therefore share the same phase information as the fundamental. An ordinary 2nd order harmonic distortion ("HD2") propagates at a multiple of 2*fundamental, now lets say that a 50Hz tone got 10% of HD2 - this equates to distortion levels of 20dB below the fundamental. Let's assume that the group delay of 50Hz is 10ms but the 100Hz group delay is 0. The HD2 will then produce a -20dB overtone at 100Hz delayed 10ms if this theory is right. This can be a issue if we go back to the point that relative phase is audible through affecting the magnitude response. Such distortion would be impossible to tune away. This is one of the theories I got about why we both preferred a vented box over a sealed even though the magnitude response was EQed to the exact same, the vented simply had lower non-linear distortion causing indivertible phase inconsistencies between fundamentals and harmonics. IF this would be the case, then group delay is certainly responsible but in combination with excessive non-linear distortion. (Sealed and vented boxes often share similar GD characteristics ~one octave around Fb, one reason you want to tune a vent low).

This is only a theory of mine and isn't proven in any way, our tests didn't involve IMD distortion adding (which is far more complicated) so that might be another factor at play here (lower HD means lower IMD generally). I still believe this is part of the puzzle though...

To get back to the original question, why should I care about a close to zero delay in the lowest frequencies?

Digital_Audio Effects (DAFx-14), Erlangen, Germany, September 1-5, 2014

This study goes through correcting the group delay of a vented box by creating a FIR inverse correction filter. Even though the listening session was "informal" they confirmed that the bass felt more defined and the subbass felt more "immersed". This is an opinion that I share after hearing proper GD corrections made by the fir based APL1 processor. This would suggest that the amount of group delay measured in the test we indeed audible, it would also suggest that the area where we are most sensitive to group delay would be the subwoofer range if we would convert the delay in milliseconds to periods/given frequency.

Without derailing too much from the original subject, you can basically have both low non-linear distortion and low linear distortion with a vented box using FIR processing. The issue would be the lengths of the actual filters, we need large IR's for any real accuracy in the lower frequencies...

I have done countless experiments using different setups, different environments etc. but I can confirm for sure that these delay corrections change the way the subwoofer sounds now. You need to hear it yourself to understand, subjective words is inadequate. I think this can be referred as the "explanatory gap". Whatever mechanic is responsible for this effect is beyond me at this point.
 

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Discussion Starter · #20 ·
For the next part we shall take some real world examples and see what we can correct using normal IIR filter and what FIR filtering can do. I need to do some more measuring in the garage before continuing, hopefully tomorrow ;)
 
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