REW-Good Looking Freq Response Graph Doesn't Tell The Whole Story - Random Thoughts/Findings & Lessions Learned

[bibo01]

13 hours ago, cjf said:

Hello,

 

I've recently went thru a rather long and painful "Retune/Reconfigure" process of my system due to the addition of a 3rd Sub (Rythmik F18SE) to compliment the two existing Subs (Rythmik E15HP2 SE's) I was using previously and as a result I needed to basically reconfigure the entire system. During this process I came to find out that adding an additional Sub wasn't as easy or straightforward as I originally expected.

 

My thought going into this was that I would just drop the new Sub into one of the remaining available spots in my room and leave the two previous Subs where they were. In theory this sounds all well and good but in practice it didn't work out that way at all. I came to find out that doing this ended up making a dogs breakfast of my nice looking original REW Freq Response Graph. No matter where I tried to place the new Sub things just kept getting worse so I had to clean the slate and start over from scratch.

 

I'll admit up front that I am no expert in doing this stuff and its certainly not part of my day job so this info is just based on my own experiences thus far while playing with Subs in my leisure as a hobby. I'm quite sure an expert in the field could spot issues in my new configuration and graphs and fix them no sweat but I chose to do this on my own using info found around the web from the various Forums, posted Articles/Papers and pure trial and error.

 

Back when I first added Subs to my system the whole process was rather daunting and the learning curve was quite steep. Now that I have an additional year under my belt doing all this and more experience on what I'm looking at and what to look for during the process I've come to find out that even though the work I put in previously that resulted in a rather pretty REW Freq Response Graph wasn't really telling the whole story and had several issues lurking in the background that I was unaware of all along.

 

This post is intended to show some of those issues I was unaware of and to maybe help others keep an eye out for them should they decide to jump into this process with blinders on like I did a few years back. Now onto the findings....

 

All graphs showing the "Original" configuration was while using 2 X Rythmik E15HP2 SE Subs located at the back of my listening room. One Sub was in the far Left corner and the other was in the far Right corner of the room. Both Subs were firing straight ahead towards the Front Wall where my main towers are located. Below is a rough diagram of the Original Sub placement in the room along with the approx Volume of the space. This was generated with the REW Simulation feature

 

Config # 1 - Original 2 Sub Placement In Room (S1 & S2 are the Rythmik E15HP2 SE's)

 

Config #2 - New 3 Sub Placement In Room (S1 & S3 are the Rythmik E15HP2 SE's) (S2 is the Rythmik F18SE)

 

Lets start off with a comparison Graph of the Freq Response between the two room/sub layouts shown above
 

• 3 measurements at the Top of the graph are the "Original" 2 Subs Config #1). 1/12th Smoothing in effect
• 3 measurements at the Bottom of the graph are the "New" 3 Sub Config #2) 1/12th Smoothing in effect

 

As you can see, the 2 Sub layout in Config #1 measured quite nicely from a in room Freq Response standpoint. I can tell you I spent over 100hrs trying to duplicate or better that Top measurement trio while re-tuning the room with 3 Subs. In short, it never happened and I was quite disturbed, annoyed and many curse words where thrown around along the way.

 

So much to my dismay I added a 3rd quite massive Sub to the room and for some reason I couldn't understand why, no matter what I did or where I placed all of the Subs, I couldn't better or even match that "Original" in room measurement with 2 Subs. Despite this though, the new 3 Sub configuration sounded significantly better in all areas across the board and especially in the tactile feel and scale categories. It wasn't even close in how the two layouts sounded. Config #2 was a clear winner.

 

Now I will introduce some of the very recently discovered demons that were lurking under the covers of that Config #1 layout with 2 Subs that I didn't realize at the time. After banging my head against the wall for a few weeks I decided to circle back and take a very hard/close look at REW again to compare the two configurations side by side.

 

Lets start this segment off with the ugliest of my findings when comparing Config #1 vs Config #2

 

Spoiler...DISTORTION For Days!!

 

All Channels Distortion Overlay (Left/Right & All Subs)

 

• Config #1 w / 2 Subs = Blue Line, Crosshair located at highest THD Peak 45.8% @ 17hz
• Config #2 w / 3 Subs = Pink Line, Crosshair located @ 17hz, THD 5.5%
• But wait...it gets MUCH Worse

 

Right Channel Distortion Overlay (Right CH Only & All Subs)

 

• Config #1 w / 2 Subs = Green Line, Crosshair located at highest THD Peak 417% @ 19hz  🤯
• Config #2 w / 3 Subs = Red Line, Crosshair located @ 19hz, THD 2.74%

 

 

So it appears that I was pushing the original Subs a bit too hard and got a bit Ham fisted with the output/loudness of the sweep settings in general. Lets take a look at a few other signs of this

 

Spectrogram Graph Comparison - All Channels (Left/Right & All Subs)
 

• Config #1 w / 2 Subs - Looking pretty HOT in here across the board but especially below 75hz with lots of far reaching overhang trails in the bass region

 

 

• Config #2 w / 3 Subs - Waaay cooler across the board but with plenty of energy still down to 10hz and below. Long overhand trials in the bass region look much better

 

So what did I do differently between the first few Graphs shown so far from the Original vs the New Configuration.

 

1. In Config #2 w / 3 Subs I Level matched the Subs with the Main Tower speakers using Random Pink Noise in the bass region playing between 30-80hz to a Ref Output Level of about 75db SPL

2. In Config #1 w / 2 Subs I Level matched the Subs at the X-Over point only with the Main Tower speakers at the loudest level I would typically listen at (around 95db). So the whole system was level matched based solely on one point of the Freq scale. In hind sight, this was a bad idea 🤕

 

Now lets look at a few other problems I discovered with my original Config #1

 

PHASE

 

Right Channel Phase Overlay (Right CH Only & All Subs)

• Config #1 w / 2 Subs = Green Line
• Config #2 w / 3 Subs = Red Line

 

 

Left Channel Phase Overlay (Left CH Only & All Subs)

• Config #1 w / 2 Subs = Orange Line
• Config #2 w / 3 Subs = Green Line
   

 

SPL/Phase Graphs

 

Config #1 w / 2 Subs, All Channels (Right/Left CH & All Subs)

• Blue Graph Line = Freq Response
• Purple'ish Graph Line = Phase ---What a mess

 

Config #2 w / 3 Subs, All Channels (Right/Left CH & All Subs)

• Pink Graph Line = Freq Response
• Brown/Green'ish Graph Line = Phase ---Way Cleaner

 

 

So it appears that there were some serious Phase anomalies going on with Config #1 in addition to it being way too hot in terms of Output Level.

 

What else did I find? Let's look at the Step Response next.

 

STEP RESPONSE
 

Config #1 w / 2 Subs, All Channels (Right/Left CH & All Subs)

 

Now with this one I'll admit that its not clear there was an issue until I took all the other findings into consideration and compared it to the new Confg #2. I can see that there is an initial Spike towards positive polarity which then goes immediately negative with a less than great matching of All the channels at the initial spike. The rest of the plot then starts from the bottom and works its way back up towards 0. Again, I'm not clear on what this really means but looking at the next Graph from Conig #2 tells me something probably wasn't right with this one

 

 

Config #2 w / 3 Subs, All Channels (Right/Left CH & All Subs)

 

We can see that this Plot is the opposite of the Original one in Config #1 and to me looks more correct based on other Step Plots I've seen around the web

 

 

Overlay of STEP RESPONSE comparing Config #1 with Config #2

 

Here in this Plot it becomes clear of the differences between the two Configs #1 vs #2

 

 

Finally to bring an end to this long original post let's look at the Impulse Response comparisons

 

Right Channel Impulse Response Overlay (Right CH Only & All Subs)

• Config #1 w / 2 Subs = Green Line - Here Config #1 appears to be showing signs of Pre-Ringing Like A Bell
• Config #2 w / 3 Subs = Red Line - Config #2 looks pretty clean by comparison
   

 

All Channel Impulse Response Overlay (Right/Left CH & All Subs)

• Config #1 w / 2 Subs = Blue Line - Here Config #1 appears to again be showing signs of Pre-Ringing Like A Bell
• Config #2 w / 3 Subs = Pink Line - Config #2 looks again pretty clean by comparison
   

 

So getting back to my original point of the post that a pretty Freq Response Graph doesn't tell the whole story of whats going on. The scary part of all this is that at no time while I was listening to my system when Config #1 was in use did I get a sense of something being wrong. The system sounded great compared to how it sounded before any subs or room correction was thrown into the mix so I was living in what is known as ignorant bliss. The Freq Response Chart looked great, things sounded great and everything sounded better than it ever had before I started this journey with room correction and subs.

 

Now that I have had a chance to directly compared the two configurations/layouts with listening and somewhat scientific measurements its become clear to me that if All the measurement data is not taken into careful consideration and your initial setup process is not don't correctly you may be wasting valuable time listening to your system with some ugliness hiding under the covers.  Even though all may seem to sound just fine.

 

I'm open to any additional dialog on this subject/info posted here including dialog that may oppose what I think seems correct now about Config #2 w/ 3 Subs compared to Config #1 w / 2 Subs

 

Thanks for reading and hopefully this helps others in their own journey of pit falls to look out for

Hi, as I was interested on your discussion, I submitted your post to Mario Bon (he is a professional Italian speaker designer and he is mostly "a man of science").  I'm giving you here his reply:

 

If, and I repeat if, a system is minimal phase or linear phase then there is a one-to-one relationship between the response in the time domain and the response in the frequency domain. This means that a flat frequency response corresponds to a flawless impulse response. In this condition, the frequency response is sufficient to characterize the system.

 

On the contrary in a mixed phase system or worse in an interference system (for example where there are several sources on different frequency bands or worse in the same frequency band but delayed between them) a flat response in steady state can correspond to a bad time response. This is the case with multi-way speaker systems (both passive and active) even worse if with many subwoofers. It follows that two measurements must be made with loudspeaker systems: the frequency response and the impulse response (either the waterfall or the wavelet or equivalent).

 

It is therefore not surprising that in the face of a flat answer the desired result is not obtained.

 

It is a mistake to expect the DRC or Dirac or whatever to work miracles. In the MiniDSP manual, for example, it is clearly written that the loudspeaker must not introduce delays between the various ways. As if to say that if the speaker does not contain defects, the system corrects those introduced by the environment. It is known that this correction implies approximations because, in theory, it would not be possible because it would have to invert a non-invertible function. To do this, the system introduces approximations. Obviously, these approximations cannot be exaggerated. Basically, the correction system must be able to understand which is the source and which are the reflections to correct.

 

The use of many subwoofers is possible but requires that the relative delay of each subwoofer must be individually adjusted (and canceled). Only in this way the DRC will be able to distinguish the source from the reflections and correct the reflections. On the 
contrary, it's a mess.

[bibo01]

On 4/26/2021 at 5:43 AM, cjf said:

Hello,

 

I've recently went thru a rather long and painful "Retune/Reconfigure" process of my system due to the addition of a 3rd Sub (Rythmik F18SE) to compliment the two existing Subs (Rythmik E15HP2 SE's) I was using previously and as a result I needed to basically reconfigure the entire system. During this process I came to find out that adding an additional Sub wasn't as easy or straightforward as I originally expected.

 

My thought going into this was that I would just drop the new Sub into one of the remaining available spots in my room and leave the two previous Subs where they were. In theory this sounds all well and good but in practice it didn't work out that way at all. I came to find out that doing this ended up making a dogs breakfast of my nice looking original REW Freq Response Graph. No matter where I tried to place the new Sub things just kept getting worse so I had to clean the slate and start over from scratch.

 

I'll admit up front that I am no expert in doing this stuff and its certainly not part of my day job so this info is just based on my own experiences thus far while playing with Subs in my leisure as a hobby. I'm quite sure an expert in the field could spot issues in my new configuration and graphs and fix them no sweat but I chose to do this on my own using info found around the web from the various Forums, posted Articles/Papers and pure trial and error.

 

Back when I first added Subs to my system the whole process was rather daunting and the learning curve was quite steep. Now that I have an additional year under my belt doing all this and more experience on what I'm looking at and what to look for during the process I've come to find out that even though the work I put in previously that resulted in a rather pretty REW Freq Response Graph wasn't really telling the whole story and had several issues lurking in the background that I was unaware of all along.

 

This post is intended to show some of those issues I was unaware of and to maybe help others keep an eye out for them should they decide to jump into this process with blinders on like I did a few years back. Now onto the findings....

 

All graphs showing the "Original" configuration was while using 2 X Rythmik E15HP2 SE Subs located at the back of my listening room. One Sub was in the far Left corner and the other was in the far Right corner of the room. Both Subs were firing straight ahead towards the Front Wall where my main towers are located. Below is a rough diagram of the Original Sub placement in the room along with the approx Volume of the space. This was generated with the REW Simulation feature

 

Config # 1 - Original 2 Sub Placement In Room (S1 & S2 are the Rythmik E15HP2 SE's)

 

Config #2 - New 3 Sub Placement In Room (S1 & S3 are the Rythmik E15HP2 SE's) (S2 is the Rythmik F18SE)

 

Lets start off with a comparison Graph of the Freq Response between the two room/sub layouts shown above
 

• 3 measurements at the Top of the graph are the "Original" 2 Subs Config #1). 1/12th Smoothing in effect
• 3 measurements at the Bottom of the graph are the "New" 3 Sub Config #2) 1/12th Smoothing in effect

 

As you can see, the 2 Sub layout in Config #1 measured quite nicely from a in room Freq Response standpoint. I can tell you I spent over 100hrs trying to duplicate or better that Top measurement trio while re-tuning the room with 3 Subs. In short, it never happened and I was quite disturbed, annoyed and many curse words where thrown around along the way.

 

So much to my dismay I added a 3rd quite massive Sub to the room and for some reason I couldn't understand why, no matter what I did or where I placed all of the Subs, I couldn't better or even match that "Original" in room measurement with 2 Subs. Despite this though, the new 3 Sub configuration sounded significantly better in all areas across the board and especially in the tactile feel and scale categories. It wasn't even close in how the two layouts sounded. Config #2 was a clear winner.

 

Now I will introduce some of the very recently discovered demons that were lurking under the covers of that Config #1 layout with 2 Subs that I didn't realize at the time. After banging my head against the wall for a few weeks I decided to circle back and take a very hard/close look at REW again to compare the two configurations side by side.

 

Lets start this segment off with the ugliest of my findings when comparing Config #1 vs Config #2

 

Spoiler...DISTORTION For Days!!

 

All Channels Distortion Overlay (Left/Right & All Subs)

 

• Config #1 w / 2 Subs = Blue Line, Crosshair located at highest THD Peak 45.8% @ 17hz
• Config #2 w / 3 Subs = Pink Line, Crosshair located @ 17hz, THD 5.5%
• But wait...it gets MUCH Worse

 

Right Channel Distortion Overlay (Right CH Only & All Subs)

 

• Config #1 w / 2 Subs = Green Line, Crosshair located at highest THD Peak 417% @ 19hz  🤯
• Config #2 w / 3 Subs = Red Line, Crosshair located @ 19hz, THD 2.74%

 

 

So it appears that I was pushing the original Subs a bit too hard and got a bit Ham fisted with the output/loudness of the sweep settings in general. Lets take a look at a few other signs of this

 

Spectrogram Graph Comparison - All Channels (Left/Right & All Subs)
 

• Config #1 w / 2 Subs - Looking pretty HOT in here across the board but especially below 75hz with lots of far reaching overhang trails in the bass region

 

 

• Config #2 w / 3 Subs - Waaay cooler across the board but with plenty of energy still down to 10hz and below. Long overhand trials in the bass region look much better

 

So what did I do differently between the first few Graphs shown so far from the Original vs the New Configuration.

 

1. In Config #2 w / 3 Subs I Level matched the Subs with the Main Tower speakers using Random Pink Noise in the bass region playing between 30-80hz to a Ref Output Level of about 75db SPL

2. In Config #1 w / 2 Subs I Level matched the Subs at the X-Over point only with the Main Tower speakers at the loudest level I would typically listen at (around 95db). So the whole system was level matched based solely on one point of the Freq scale. In hind sight, this was a bad idea 🤕

 

Now lets look at a few other problems I discovered with my original Config #1

 

PHASE

 

Right Channel Phase Overlay (Right CH Only & All Subs)

• Config #1 w / 2 Subs = Green Line
• Config #2 w / 3 Subs = Red Line

 

 

Left Channel Phase Overlay (Left CH Only & All Subs)

• Config #1 w / 2 Subs = Orange Line
• Config #2 w / 3 Subs = Green Line
   

 

SPL/Phase Graphs

 

Config #1 w / 2 Subs, All Channels (Right/Left CH & All Subs)

• Blue Graph Line = Freq Response
• Purple'ish Graph Line = Phase ---What a mess

 

Config #2 w / 3 Subs, All Channels (Right/Left CH & All Subs)

• Pink Graph Line = Freq Response
• Brown/Green'ish Graph Line = Phase ---Way Cleaner

 

 

So it appears that there were some serious Phase anomalies going on with Config #1 in addition to it being way too hot in terms of Output Level.

 

What else did I find? Let's look at the Step Response next.

 

STEP RESPONSE
 

Config #1 w / 2 Subs, All Channels (Right/Left CH & All Subs)

 

Now with this one I'll admit that its not clear there was an issue until I took all the other findings into consideration and compared it to the new Confg #2. I can see that there is an initial Spike towards positive polarity which then goes immediately negative with a less than great matching of All the channels at the initial spike. The rest of the plot then starts from the bottom and works its way back up towards 0. Again, I'm not clear on what this really means but looking at the next Graph from Conig #2 tells me something probably wasn't right with this one

 

 

Config #2 w / 3 Subs, All Channels (Right/Left CH & All Subs)

 

We can see that this Plot is the opposite of the Original one in Config #1 and to me looks more correct based on other Step Plots I've seen around the web

 

 

Overlay of STEP RESPONSE comparing Config #1 with Config #2

 

Here in this Plot it becomes clear of the differences between the two Configs #1 vs #2

 

 

Finally to bring an end to this long original post let's look at the Impulse Response comparisons

 

Right Channel Impulse Response Overlay (Right CH Only & All Subs)

• Config #1 w / 2 Subs = Green Line - Here Config #1 appears to be showing signs of Pre-Ringing Like A Bell
• Config #2 w / 3 Subs = Red Line - Config #2 looks pretty clean by comparison
   

 

All Channel Impulse Response Overlay (Right/Left CH & All Subs)

• Config #1 w / 2 Subs = Blue Line - Here Config #1 appears to again be showing signs of Pre-Ringing Like A Bell
• Config #2 w / 3 Subs = Pink Line - Config #2 looks again pretty clean by comparison
   

 

So getting back to my original point of the post that a pretty Freq Response Graph doesn't tell the whole story of whats going on. The scary part of all this is that at no time while I was listening to my system when Config #1 was in use did I get a sense of something being wrong. The system sounded great compared to how it sounded before any subs or room correction was thrown into the mix so I was living in what is known as ignorant bliss. The Freq Response Chart looked great, things sounded great and everything sounded better than it ever had before I started this journey with room correction and subs.

 

Now that I have had a chance to directly compared the two configurations/layouts with listening and somewhat scientific measurements its become clear to me that if All the measurement data is not taken into careful consideration and your initial setup process is not don't correctly you may be wasting valuable time listening to your system with some ugliness hiding under the covers.  Even though all may seem to sound just fine.

 

I'm open to any additional dialog on this subject/info posted here including dialog that may oppose what I think seems correct now about Config #2 w/ 3 Subs compared to Config #1 w / 2 Subs

 

Thanks for reading and hopefully this helps others in their own journey of pit falls to look out for

Another contribution from DRC expert Tom Capraro to your question from the same forum:

 

Looking at the graph of the frequency response, I don't understand why the author of the thread is so happy about those frequency responses.
There is a scale represented in 10dB steps, moderately "compressed", and the trend of that curve would produce - basically - an unbalanced sound: muffled in the top three lines and "without bass" in the bottom three lines.
Apart from the fact that a system in the environment is not minimum phase (but excess phase), they seem to me to be approximate frequency responses and with a lot to improve.
Even if a frequency response had a psychoacoustic trend, it would appear, if represented in 10dB steps, to be almost a ruler.
The performance of a psychoacoustic curve is already at the limit, that is to say it is a curve that points towards high SPL listening.

[bibo01]

51 minutes ago, cjf said:

Are they saying my system is broke?

No, they are not saying that.

They mostly say that your measurements are incomplete with space for improvement. For example, the scale of your frequency response graph has too wider steps to show "problems" properly.

Did you apply delay for each subwoofer?

Anyhow, I asked them directly on the Italian thread what measurements and in general what you should do differently to improve/adjust your system. 

 

If you don't understand some passage, let me know, perhaps it's my fault as something might have been lost in translation   

 

PS: of course, you can Google translate and contribute directly to "your" Italian discussion.

[bibo01]

2 hours ago, cjf said:

In terms of the zoom level of the first Freq Resp chart I'm not sure if adding additional hash marks is possible or not but I can say the largest dip/spike at the worst point is about 10db.

Relative to the frequency response, Tom Capraro replies that it is not a question of dip/spike, but of trend.
Between the first segment (up to about 200Hz) and the harmonic area (from 1500Hz upwards) there is a drastic and sudden drop with a difference in attenuation between 10dB and 15dB.
Such a curvature kills the harmonic rendering of the sound.

[bibo01]

9 hours ago, cjf said:

Below is a graph showing the Group Delay of the system in its current state (ie..3 Subs Config#2).

 

All Channels appear to line up pretty nicely for the most part. The delays of all channels to the Main Listening position are taken into consideration when the correction filters are created.

 

Here it seems that at around 70 Hz group delay is over 100 ms.
In 100 ms sound travels 34.4 meter whilst at 70 Hz a wavelength is about 5 meter (4.9143 m).

Food for thought...

[bibo01]

@cjfTom Capraro, trying to understand what you feel is strange in your system, is asking "what do you feel is wrong as you listen?"
Furthermore, if you can make mdat files available, he will be able to observe your measurements better.

[bibo01]

44 minutes ago, cjf said:

Hello,

 

I'm getting the sense that there is a misunderstanding occurring. The original intent of my post was to show that if one only considers the Feq Resp curve in a room measurement and not all the other measurements they may be overlooking other issues that could still be there even though the Freq Resp curve looks OK, good or even great.

 

I do not think that anything sounds wrong or strange with the system as it sits today which is represented as Config #2 in all the graphs previously posted.

 

If one looks at basically any in room speaker measurement found on "pick your favorite audio rag" you see all sorts of uneven spikes/dips and drastic drop offs at various points in the curve. Even with the uber priced super speaker going for hundreds of thousands of dollars. In most cases you see a large bump at 20hz or higher that drops off above and below that +10 to +20db mountain which in my opinion may be fine for those who never actually crank up their system to elevated levels. I suspect the speaker manufacturers do this on purpose so that when listening at low levels it gives a greater sense of bass output. But for those who do crank up the volume of their system the same Freq Resp graph sounds like a 1980's boom box.

 

Its been my understanding that the ultimate goal of any speaker manufacturer would be to have their speaker's Freq Resp look like a perfectly straight line. This goal has not been achieved in any measurement I've ever seen. Such a speaker would be able to reproduce the source material perfectly without adding its own flavor to the original sound. Then you add such a speaker to a real room. At that point all bets are off on what the Freq Resp graph will look like.

 

The fact that my measurements show a roughly 10-12db roll off at each extreme doesn't seem all that bad and in fact matches pretty closely with just my tower speakers alone and no room correction or subs. The biggest difference between Config #2 and a measurement of just the Main towers alone in this same room is that the current measurement has usable bass extension and output down into the single digits.

 

The room this system is located in is quite large (at least 4500cu/ft) for just the listening area alone and very open to other areas of the house as well. In order to fill this space with sound to make the Freq Resp chart have the very typical 10-20+ dB mountain seen in many in room measurements previously mentioned it would take far more cubic inches of Sub and power to go with it. In any case, a Freq Resp chart that looks like that is not what I prefer to hear. I'm not interested in artificial bloom or bass texture that one note sounding due to excessive overhang as a result of again that typical chart seen in the audio rags.

 

With all that said though, I do have the ability to alter the shape of the Freq Resp curve until I'm blue in the face using Audiolense. But this circles back to one of the issues previously shown in my original Config #1 layout with the better looking Freq Resp chart. The end result of trying to reproduce that better looking Freq Resp chart being way higher levels of distortion requiring me to push the Subs outside of their limitations in terms of being able to maintain good SQ at louder listening levels.

 

I can say for sure there is no lack of bass or detail in the current configuration. I don't think it even makes sense to suggest a -10db roll off from the highest peak at around 100hz or so down to 14hz and below while still outputting over 80db+ down there would have a lack of bass output. Even most of those uber mega buck speakers can be down 10-30db or more after 20hz if your lucky.

 

I guess it all comes down to personal preference. I like my sound to be as unflavored as possible and as loud as possible whenever possible.

 

 

OK, fine. I'll stop here.

So you were very happy with your #1, but when #2 arrived you realized that you were "living in an ignorant bliss".

It seems to me that now you are happy "living an ignorant bliss #2". As you are happy, however, it's fine by me and I will not waste my time any further. 

[bibo01]

2 hours ago, Jud said:

bibo, I am not sure exactly what is meant by a "one-to-one relationship."

The Italian original version was "relazione biunivoca".

In mathematics: one-to-one correspondence, the correspondence between two sets of objects, when one and only one quantity of the second set corresponds to each size of the first set and vice versa.

[bibo01]

7 hours ago, Jud said:

If the system is linear phase (not very common, since there is an unavoidable frequency response bump if a crossover is designed to be linear phase - this is the case with my speakers), then the relationship between frequency and timing/phase is indeed linear, so that could be what is meant by a "one-to-one relationship."  However, with minimum phase, the relationship between frequency and timing/phase is *not* linear, and so I am puzzled as to what "one-to-one relationship" means in this case.

 

If it is possible, would you be able to ask your friend, who surely knows more than I do about this?

Mario Bon replies:

 

There is always a lot of confusion between the meaning of minimum phase and linear phase.
In minimum phase systems there is the possibility to determine the transfer function knowing only its amplitude (modulus of the frequency response) or only its phase. So not only is there a 1-to-1 relationship between time response and frequency response but also between amplitude response and phase response.
In linear phase systems it is not possible to derive the frequency response from the phase response because this contains only one piece of information (the constant group delay). So you need to know the frequency response. There remains the 1-to-1 correspondence between response in time and response in frequency.

 

Networks or those stuff made with resistors, capacitors, inductors and transformers that do not use all-pass networks and where the path between input and output is unique are minimum phase. It follows that speaker systems, if they have no defects, are minimum phase systems.