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Step Response: Does It Really Matter?

watchnerd

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#61
I agree about measurements, but I don't think it is that complicated. I think that the designers of a certain German DSP-based speaker (that some people are sick of hearing about!) have approached the problem in full knowledge of what they were doing, and their relatively simple design just works. It wasn't put together by trial and error, and lots of listening, or even lots of measurements. It was, instead, based on predictions of the simple physics of driver dimensions, baffle sizes, and the role of DSP as 'glue'. I rather expect that their first prototype sounded better than 95% of all other 'high end' speakers within a day of them first trying it out.
It's not just that German speaker whose-name-we-dare-not-speak-least-like-Sauron-it-summon-the-sales-wraiths, there are also the crazy French guys, who seem to get more attention with the celebrity crowd, even getting their stuff listed in the Apple store:








Plus you can get a case that looks like a set of butt cheeks:

 

j_j

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#62
Hrm. Well, I'll say it again, Step Response and Impulse response are related. The only difference is that step response includes much more low-frequency energy than high-frequency energy, and Impulse Response is flat in frequency. Both measure the same thing, but with different excitation functions. Systems that use allpass signals or sweeps do the same thing as well, and the various results are all simply mathematically related.

Some things to remember about both Impulse and Step Responses.

1) if the system has no DC response (like almost any speaker, aside from the modulated-fan subwoofer in a sealed room) then the mean of the entire response must be zero.
2) The leading edge of the step response, or the sharpness of the impulse response, pretty much determines the high frequency behavior of a system.
3) the "droop" more or less defines the low frequency behavior of a system.
4) But they both tell you the same thing. You just have to adjust to the spectrum and phase of the excitation signal.

If you look for the "FFT workshop" at www.aes.org/sections/pnw in the powerpoint or meeting recap pages, you'll see some discussion on one way to measure things and get back to the impulse response with a lengthy excitation. That meeting was 3 hours to start with, so I didn't go into shaping the excitation signal, but surely one can see how :)
 
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watchnerd

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#63
Hrm. Well, I'll say it again, Step Response and Impulse response are related. The only difference is that step response includes much more low-frequency energy than high-frequency energy, and Impulse Response is flat in frequency. Both measure the same thing, but with different excitation functions. Systems that use allpass signals or sweeps do the same thing as well, and the various results are all simply mathematically related.

Some things to remember about both Impulse and Step Responses.

1) if the system has no DC response (like almost any speaker, aside from the modulated-fan subwoofer in a sealed room) then the mean of the entire response must be zero.
2) The leading edge of the step response, or the sharpness of the impulse response, pretty much determines the high frequency behavior of a system.
3) the "droop" more or less defines the low frequency behavior of a system.
4) But they both tell you the same thing. You just have to adjust to the spectrum and phase of the excitation signal.

If you look for the "FFT workshop" at www.aes.org/sections/pnw in the powerpoint or meeting recap pages, you'll see some discussion on one way to measure things and get back to the impulse response with a lengthy excitation. That meeting was 3 hours to start with, so I didn't go into shaping the excitation signal, but surely one can see how :)
I understand the mathematical relationship between FFT / impulse / step response.

What I'm not so clear on is if the visualization of time alignment that the step response is good at displaying correlates with subjective quality. Even John Atkinson seems to say it has a low correlation (which makes me wonder why he bothers to measure it).

Next question, though:

How how related are the step / impulse response of a system to a cumulative decay response?



My gut instinct is that if the anomalies of a cumulative decay response are related to electromechanical resonances, they would be related, but if they're related to box resonances, they would be less related.
 

j_j

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#64
How how related are the step / impulse response of a system to a cumulative decay response?

My gut instinct is that if the anomalies of a cumulative decay response are related to electromechanical resonances, they would be related, but if they're related to box resonances, they would be less related.
Why would that matter? Unless the system is time varying or highly nonlinear (i.e. a Leslie cabinet on high spin, or just plain busted), they are exactly related.
Electromechanical resonances are usually minimum phase, and have the form of a decaying sine wave. Their responses will usually be a line in log-frequency, i.e. db/octave.
Box reflections are not minimum phase in general, and look more like comb filters. They can be either all pole, all zero, or some of both, but their peaks/dips will be uniformly spaced in frequency for every reflection. db/octave is not necessarily the best way to evaluate their performance, however.

This is related to the difference between filters in the "analog" domain, whose responses are best modelled in the log frequency space, and digital filters, whose response is better modeleld in the linear frequency space.

sdomain.jpg

This is an example of a bandpass filter in the analog domain. Notice how it has a response that is symmetric in the log-frequency domain, and you can see the 18db/octave spectral slope overall.
zdomain.jpg

And this is a filter in the delay-domain (z domain). It is digital but physical filters using delays have exactly the same symmetry, which, you notice, is in the linear frequency domain.

That is the big difference in filter systems.

But they are both imposed on the same system. Any issue that obscures one or the other is due to measurement differences, not to anything else.

The time/frequency plot of energy will be different for the different systems, of course, but I'm not sure why you think one would be more or less related, they are both measured int the same system.

It is true that comb filters and second-order all-poll filters will have different responses. That doesn't mean one is more or less related to results.
 
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Cosmik

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#65
OK, inspired by this thread I have measured the step response of my home made, sealed, DSP-based, three-way active speakers.

This is the step response measured at 1m at tweeter height hopefully free of reflections, and after the processing that, technically, is designed for the listening position, notably delays for time alignment. As I mentioned in another thread, I haven't actually bothered with this before, relying on time alignment 'by inference' based on driver phase correction derived from individual driver measurements plus delays by calculation. There is also in-room EQ designed to compensate for baffle step, tuned by ear, and bass extension EQ (lowering the start of roll-off) by calculation. Without any cheating I am suprised at how close to a step I have got:
upload_2017-10-16_10-27-24.png
 

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#66
Olive / Toole think it's not that important.

Or, to put it differently, it ranks much much lower than flat-ish amplitude and controlled directivity in their testing.
I tend to concur with this, although I do think step response has some influence, although where it resides in the hierarchy I am not sure.

Using Acourate, with my Linkwitz LX521s I can get a very good step response at the expense of some group delay at about 90Hz. I can adjust Acourate and lower the group delay to a level where I think it would be inaudible at the expense of a poorer step response. Subjectively, I prefer the good step response setting, but the difference is quite subtle. However, I do think that the overall improvement I'm getting is more to do with Acourate flattening the amplitude and the directivity of the Linkwitz upper baffle than the improved step response.

Here's a prototype measurement from the Linkwitz lab site showing the LX521's on axis and off axis response.

LX_mid-tweeter_eq_uppermid-axis-50cm-300.png
 
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mitchco

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#67
Is optimizing for superior time-alignment actually an unimportant design goal?
This is an area where more DBT research should be updated as more powerful computers and DSP software have made time aligning drivers a fairly easy task, to a level of accuracy and precision previously unheard of. In my experiments in time aligning drivers, with different speaker systems, and playing with different delay values between drivers, I find it does make an audible difference. Some proponents like Rod Elliot, who set out to debunk time alignment, now think all speakers should be time aligned: "For what it's worth, I originally started this article not to praise, but to debunk the theory that time alignment is the only way a speaker should ever be designed. Having done the research, run tests, and written the article, I confess that I must agree with many (perhaps even most) of the points made by the time alignment proponents. My overall opinion, based on the research for this article (primarily tests and simulations), is that time alignment is a very good thing, and perhaps all speakers should be designed this way." From: http://sound.whsites.net/ptd.htm

The step response is a good measurement to not only identify time alignment, but other aspects as well, which are also audible, at least in my experiments. Take this example, where I have time aligned a 2-way system using Audiolense 5 and then only changed one parameter: more low frequency correction at the listening position and tooo another measurement. Nothing else has changed, levels the same, mic position same, etc. This is using a linear phase digital XO FIR filter:



The red and blue have less low frequency correction versus the green and magenta. If one switches to a group delay view of the same chart:



Note the increase in group delay with less low frequency correction for the red and blue traces. And corresponding phase display, again at the listening position:



Is it audible? To my ears it is. I can switch the two level matched FIR filters in real time listening to music and readily pick out the filter with less group delay below 100 Hz. To my ears, the bass has more weight and sounds in phase with the rest of the music, is the subjective evaluation, even through there are currently no DBT's showing one can hear group delay below 100Hz...

Which is why I suggest more testing of time alignment and group delay properties using DBT's would be an interesting area of research to embark on, given the power of computers and sophisticated DSP that did not exist ten years ago.

Part of my point is the comparison of the two step responses and that there is an audible difference between them. Looking at what @watchnerd posted for step responses, some of them are wildly different, and I would expect an audible difference for sure. I believe part of the issue is that many reviewers may not have heard a legitimately time aligned system and therefore have no reference to compare or have not taken the time to educate ones ears by AB'ing FIR filters with different levels of delay between drivers and tuning into what that sounds like... Just like all things, once one tunes into what dials are being adjusted and what it sounds like, and becomes aware, it is no longer a subtle difference. However, it is indeed complicated, with a lot of moving parts to keep track of to ensure only one parameter under test is actually being varied...
 

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Cosmik

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#68
I believe part of the issue is that many reviewers may not have heard a legitimately time aligned system and therefore have no reference to compare or have not taken the time to educate ones ears by AB'ing FIR filters with different levels of delay between drivers and tuning into what that sounds like...
I agree. Someone else who says the same thing:
Traditionally, when I listened to the quality of the sound reproduced by my audio playback equipment, I focus on tonal balance (frequency response), dynamics of the sound (SNR), residual noise floor ( inaudible ), distortion ( inaudible ). Interestingly, all of the above characteristics can be assessed and visualized in frequency domain. It was simply the easiest way to listen to the sound and evaluate what I was hearing, but I now realize, that I was only considering the steady-state analysis in the frequency domain...

...I was doing the same type of analysis over, and over again for years, and grew accustomed to this ritual. It was easy to compare with measured results, so it felt comfortable, that I can correlate my measurements with what I can easily hear (or can not hear). Recently, things have changed for me. ...and as a result I came to the conclusion, that my listening tests were only a starting point of what I should have listened to when examining linear-phase loudspeakers. To put it simply – I needed to significantly extended the evaluation of time domain characteristics of the loudspeaker in my listening habits....

...The remaining part of this paper is my crude attempt to summarise audible attributes of linear-phase loudspeakers.... It clearly points to the time-domain characteristics of the loudspeaker, and this is something, which may of us (till recently, including myself) are not accustomed to. I simply did not know what to listen for.
 

watchnerd

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#69
OK, inspired by this thread I have measured the step response of my home made, sealed, DSP-based, three-way active speakers.

This is the step response measured at 1m at tweeter height hopefully free of reflections, and after the processing that, technically, is designed for the listening position, notably delays for time alignment. As I mentioned in another thread, I haven't actually bothered with this before, relying on time alignment 'by inference' based on driver phase correction derived from individual driver measurements plus delays by calculation. There is also in-room EQ designed to compensate for baffle step, tuned by ear, and bass extension EQ (lowering the start of roll-off) by calculation. Without any cheating I am suprised at how close to a step I have got:
View attachment 9380
Holy crapola Batman, that's pretty damn good! Better than a huge swath of commercial designs!

May I ask what the drivers are and what DSP you're using?
 

watchnerd

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#70
This is an area where more DBT research should be updated as more powerful computers and DSP software have made time aligning drivers a fairly easy task, to a level of accuracy and precision previously unheard of. In my experiments in time aligning drivers, with different speaker systems, and playing with different delay values between drivers, I find it does make an audible difference. Some proponents like Rod Elliot, who set out to debunk time alignment, now think all speakers should be time aligned: "For what it's worth, I originally started this article not to praise, but to debunk the theory that time alignment is the only way a speaker should ever be designed. Having done the research, run tests, and written the article, I confess that I must agree with many (perhaps even most) of the points made by the time alignment proponents. My overall opinion, based on the research for this article (primarily tests and simulations), is that time alignment is a very good thing, and perhaps all speakers should be designed this way." From: http://sound.whsites.net/ptd.htm

The step response is a good measurement to not only identify time alignment, but other aspects as well, which are also audible, at least in my experiments. Take this example, where I have time aligned a 2-way system using Audiolense 5 and then only changed one parameter: more low frequency correction at the listening position and tooo another measurement. Nothing else has changed, levels the same, mic position same, etc. This is using a linear phase digital XO FIR filter:



The red and blue have less low frequency correction versus the green and magenta. If one switches to a group delay view of the same chart:



Note the increase in group delay with less low frequency correction for the red and blue traces. And corresponding phase display, again at the listening position:



Is it audible? To my ears it is. I can switch the two level matched FIR filters in real time listening to music and readily pick out the filter with less group delay below 100 Hz. To my ears, the bass has more weight and sounds in phase with the rest of the music, is the subjective evaluation, even through there are currently no DBT's showing one can hear group delay below 100Hz...

Which is why I suggest more testing of time alignment and group delay properties using DBT's would be an interesting area of research to embark on, given the power of computers and sophisticated DSP that did not exist ten years ago.

Part of my point is the comparison of the two step responses and that there is an audible difference between them. Looking at what @watchnerd posted for step responses, some of them are wildly different, and I would expect an audible difference for sure. I believe part of the issue is that many reviewers may not have heard a legitimately time aligned system and therefore have no reference to compare or have not taken the time to educate ones ears by AB'ing FIR filters with different levels of delay between drivers and tuning into what that sounds like... Just like all things, once one tunes into what dials are being adjusted and what it sounds like, and becomes aware, it is no longer a subtle difference. However, it is indeed complicated, with a lot of moving parts to keep track of to ensure only one parameter under test is actually being varied...
Thank you for the very detailed post.

Do you feel like the audibility of time alignment is most subjectively perceived in the bass?

I have to admit, at first I find that surprising, given my understanding that our hearing acuity for bass anomalies is pretty poor.

Then again, maybe given room interactions with the bass, time alignment somehow helps?
 

watchnerd

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#71
The time/frequency plot of energy will be different for the different systems, of course, but I'm not sure why you think one would be more or less related, they are both measured int the same system.
I was thinking specifically of high-Q enclosure resonances that are excited only under particular circumstances that may not be agitated (or not much) under normal circumstances, but will ring like a proverbial bell with the right catalyst.
 

Cosmik

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#72
Holy crapola Batman, that's pretty damn good! Better than a huge swath of commercial designs!

May I ask what the drivers are and what DSP you're using?
That's very nice of you to say so. The drivers are almost the cheapest you can buy. No-name 8" bass driver, Monacor 3" mid and Monacor 1" tweeter.

The DSP is software I wrote myself (in 'C', based around an open source FFT library, running in Linux), and the aim is to make each driver linear phase, apply the right delay and gain to each driver, then decide upon the two crossover frequencies and slopes - there's a wide range of settings where you simply don't hear a change when applied. (For the above measurement it was crossovers at 300Hz and 3kHz both 4th order slope, generic 'smooth shape').

There's also a baffle step compensation curve calculated from the baffle width whose depth I set by ear, and as I mentioned an extension to the bass roll-off, taking it from its natural point down to 38 Hz. Reluctantly, I am experimenting with bass room compensation but for the above measurement this was turned off. As you may have gathered, I am not an adherent to the philosophy of 'room correction'!

The crossover function and all of these additional curves and compensations are overlaid onto a single filter for each driver. The delays are created separately in the time domain with offsets in the sample buffer addressing.
 
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watchnerd

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#73
As you may have gathered, I am not an adherent to the philosophy of 'room correction'!
I've lately been wondering how much psychacoustic research has been done on room correction.

I know the flat curves look nice.

But there are so many methods (REW, Dirac, Anthem, etc.), presumably using different models, but I haven't seen much testing as to which is the best, in in blind listening tests. Or any/all of them vs no correction.
 

Jakob1863

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#74
I think this is the moment to come clean: I have never really understood this "step response" thing. I've tried to read about it, but it's still fuzzy to me. It's still unclear after this thread.

Could someone please have patience with me and make a "step response for dummies" explanation, using layman terms? :)
I don´t know if it will help, but i give it a try. :)

1.) Basics / Theory

It is based on system theory. We know that for a LTI-system (linear and time invariant system) all we have to know is the response of the system to an impulse input.
From that we are able to calculate the response of this system to every other input signal. (Any input signal that the system is able to work with)

The step response is linked in a bijective way to the impulse response of the system, so if we know the step response of a LTI-system we again are able to calculate the response of this system to any other input signal

2.) Basics / Reality

no system is really a linear and time invariant and we are not able to realize an impulse input (which should be a Dirac pulse to comply fully with the theory) so we are bound to approximations.
In reality even a non Dirac impulse is difficult to realize and to capture the response of the system in a sufficient way is still difficult (j_j mentioned in a post above the signal to noise ratio for example).

Using a step response is easier to do and delivers, as said above, the same information.

But still a difficult task, so other variants were developed to overcome at least some of the difficulties; one way was the mentioned MLS (maximum length sequence) the more modern variant is the sweep sine invented by Farina. If these signals are linked in a bijective way to the step response (and therefore to the impulse response) they still deliver the same information (although mathematics get more complicated) which means that we are still able to calculate the response of the LTI-system to any other input signal.

All methods have their specific constraints and advantages so the user has to choose the right on for the specific task.
 

Jakob1863

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#75
<snip>
How how related are the step / impulse response of a system to a cumulative decay response?



My gut instinct is that if the anomalies of a cumulative decay response are related to electromechanical resonances, they would be related, but if they're related to box resonances, they would be less related.
I don´t know if i understand your question correctly, but the cumulative decay display is just another visualization of the information contained in the impulse response/step response. It is just a matter of convenience, but it the resolution of a step response graphic is good enough you would be able to calculate/retrieve the decay information "manually" too.
 

Jakob1863

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#76
Before the advent of modern DSP crossovers, I would have said the 'no crossover in the listening range' was one of the killer attributes of electrostats.

But, these days, with active DSP speakers being as good as they are, I just don't see that as such a big advantage anymore. Tying this all back to the thread, below is the step response for the Dynaudio Focus XD 200, with its DSP crossover / EQ:



Those results are simply superb. If step response matters, that result is superior to any measured hybrid electrostat I've seen.

The spectral decay is equally great. These are not vibratory monkey coffins of yore:



(All graphs courtesy of Stereophile)

Unless I subjectively prefer the radiation pattern of panel speakers, I don't see any objective reason these days to prefer them to digitally EQed multi-way dynamic speakers. Some of the biggest advantages of panels (lack of crossover, good impulse response) can now be addressed digitally in dynamic speakers.
I share you favour of (big) electrostatic panels and still think that some of their strengths aren´t yet to find in even the most refined "normal" speakers, but that holds true even if some crossover parts were included. See for example electrostats using just a small part of the panel for high frequency reproduction or the quite complicated network in Quads.

And the decay looks often quite chaotic in these large panels but nevertheless there is something very appealing to their performance; iow for me there is a certain sort of realism delivered that i don´t find in other speakers.

I've lately been wondering how much psychacoustic research has been done on room correction.

I know the flat curves look nice.

But there are so many methods (REW, Dirac, Anthem, etc.), presumably using different models, but I haven't seen much testing as to which is the best, in in blind listening tests. Or any/all of them vs no correction.
Beside the experiments done by Harmon there isn´t so much available. A lot of the room acoustic stuff isn´t evaluated by strict controlled listening experiments which is imo related to the tremendous effort needed...

Edit: What is the name of the german speaker that we shall not speak aloud? :)
 

mitchco

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#77
Thank you for the very detailed post.

Do you feel like the audibility of time alignment is most subjectively perceived in the bass?

I have to admit, at first I find that surprising, given my understanding that our hearing acuity for bass anomalies is pretty poor.

Then again, maybe given room interactions with the bass, time alignment somehow helps?
Here is a step response of a JBL 4722 two way cinema speaker without time alignment:



Here we notice that the woofer (low rise) is arriving before the tweeter (sharp spike). This is normal for a horn loaded top end as the acoustic centre of the compression driver/horn combo is about 8" in physical distance behind the acoustic centre of the woofers. Usually it is the tweeter to first arrive at the mic or one's ear in a typical cone 2 or 3 way speaker system. Folks wonder why when they try and eq a system, where the tweeter arrives first, that it does not sound right - eq can't fix a driver time alignment issue. Anyway, this amount of time misalignment can be heard readily to my ears in a quick AB test comparing this non-time aligned filter with one that is time aligned. Another giveaway is to stand up and hear the comb filtering while music is playing aside from the odd imaging.

I replaced the amplifier that was driving the bass section on this two way and measured the step response again:


What's happening here? Now the tweeter (spike) is arriving before the woofer. It tuns out that the Crown XLS 1502 amp I installed uses DSP, even if all bypassed, introduces about 60 samples of delay measured at 48 kHz. Listening to this reminds of other speakers where the tweeter arrives first and the bass sounds disconnected. Forward sounding... and readily audible, especially if you have heard a legitimately time aligned system before.

Just to finish off, here is the two way time aligned, along with the "target" or "ideal" step response. Just like Toole/Olive/Harman suggests a target frequency response, I believe there is also a target timing response, or the best one can get in a non anechoic environment, but that is for another discussion.



Switching to the topic of so called "room" correction, this is where the DSP software time domain correction can envelope a couple of non-minimum phase reflections in the bass. These low frequency reflections exist in virtually any typical living room simply based on the dimensions of the room... The impulse inside the time window is corrected towards the time domain behaviour of the target response.

Posting this group delay comparison that I previously posted where the only difference is increasing the time window in the low end from 2 cycles (i.e. 200ms @ 10Hz) to 5 cycles (i.e. 500ms @ 10Hz) of correction:



The red and blue traces are the left and right speakers with 2 cycles of time domain correction and the green and magenta traces are with 5 cycles of time domain correction. As can be seen, the group delay (i.e. non-minimum phase reflections) at 50Hz and 65Hz have been reduced by almost 50ms. The reason why for the group delay peaks at different frequencies is because the left and right speakers are offset to one side of centre of the room. I don't know any other way, other than (over) stuffing the room with absorption or really large diffusers, that one can negotiate this non-minimum phase behaviour other than using DSP "room" correction. I wish I could demo this to folks to hear it.

So to answer your questions, driver time alignment, in my listening experiments, can be heard where the frequency spectrum is divided by the number of drivers used. Each 2 or 3 or 4 way (or satellite and subs) have potential for driver time misalignment. More research into the audibility of how much time misalignment can or cannot be heard under controlled conditions would be worthwhile venture IMO. Same applies for negotiating non-minimum phase behaviour at low frequencies in a room.
 

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Fitzcaraldo215

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#78
I've lately been wondering how much psychacoustic research has been done on room correction.

I know the flat curves look nice.

But there are so many methods (REW, Dirac, Anthem, etc.), presumably using different models, but I haven't seen much testing as to which is the best, in in blind listening tests. Or any/all of them vs no correction.
Amir has cited the study linked to below many times, as have I. Amir said he thinks it is the only comparative study available of the technology using good science. It is old now, 2009 or so, and quite a few of today's best products were not yet available - I am thinking Acourate, Dirac, Trinnov, Lyngdorf, etc. But, the concept remains quite viable, and, in my view, it is absolutely indispensable. It is one of the few slam dunk sonic improvements based on good science you can get.

There are, of course, differences in the various approaches. I would not get too hung up on target curves. Any decent product will let you customize and tweak those to your heart's content, also leaving frequency ranges uncorrected if you wish.

And, flat curves are not what most products seek. They generally seek a smooth, downward sloping curve with increasing frequency which sounds psychoacoustically flat, based on empirical studies. However, the big payoff from the technology is correction of the typically large, narrow response swings of many dB in the bass below the transition point, due to room modes.

Link -

https://drive.google.com/file/d/0B9...cyLWEzZTAtMGJiODQ1ZTUxMGQ4/view?ddrp=1&hl=en#
 

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#79

Fitzcaraldo215

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#80
I discovered this study some time ago, which also compared different room correction products. Not published or peer reviewed yet, but done by serious researchers it seems: https://www.researchgate.net/public...o_The_Effectiveness_of_Active_Room_Correction

Btw, thanks for the enlightening explanations on what this step response thing is, guys. I'm closer to getting a good handle on it now!
That citation, from 2011, is, more or less, about the same study by the same authors I linked to in my prior post, above. So, as Amir said, that may be the one and only scientific study, albeit with several published summaries at different dates of the same results of the technology using available commercial products. Unfortunately, the study goes back nearly a decade in a fast moving technological field.
 
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