• The move to the new server is done. There are some software and database maintenance updates in process. This has us passing the hat around to help out. We appreciate any donations. Seriously, even a dollar helps. The payment page may be found here - https://www.audiokarma.org/support.html

Curse of the Fourier / Combinatorial Explosion

onanysunday

onanysunday

chasing realism
Subscriber
One thing that has always eluded me is why is it so hard to entirely know how a piece of audio equipment will actually sound based off its specs alone (predictively speaking). If they're truly doing their job, we should be able to rely on them 100% of the time to the point of full predictability and repeatability in sound every time when choosing equipment. However, this is not what we have and this isn't the case. For instance, what are all the specs you would point to that are responsible for stereo's ability to reproduce a phantom third center channel in stereo listening, or the width/depth of its soundfield, or how some equipment is either more natural or artificial sounding, or the forwardness or recessed nature of a given piece of equipment's soundstage? Most standard measurements we make are static or two-dimensional in nature. They're a snapshot measurement taken without the benefit of time, or the type of real world three-dimensional dynamic response that we actually hear and experience through music listening through imperfect ears with their non-linear frequency response receptivity. There are more inputs and inter-dependent relationships we don't even realize which are effecting any particular final outcome. There are other factors not yet measured that impact the sound of a piece of equipment. Since they aren't taken into consideration or haven't yet been defined through traditional testing methods that are agreed upon and widely used, our understanding of everything that goes into what we consider "sound" is not complete.

If we were to consider other performance factors that can only be measured through the passage of time, we exponentially increase the possibility of new outcomes and relationships which that additional information could provide. This is why the short and simple explanation of something taken through static measurement alone is generally not entirely correct because it doesn't take into consideration other factors that are having an effect but are not yet defined. While science is foundational to our understanding of everything, with regards to music, our understanding of all its complexities put together is still incomplete. If it were complete, we would be able to choose equipment based off agreed upon specs that lead us to a final, consistent sound every time. Unfortunately, we don't have that. We don't know everything and that's okay, because we can continue to strive to know and understand more, but we must remain humble that none of us knows everything. On top of everything happening just inside the piece of equipment itself, then combine all the other effects like inter-connected equipment, cables, wires, length of cabling, conductor and insulator types and their purity, listening space, room treatments, cleanliness or stability of voltage, bare floor or carpeted listening room, bass nodes, speaker positioning, time alignment, age of components (their new sound vs. old sound), etc. The final resulting sound anyone can achieve at any time with any particular listening rig is nuanced and almost infinite in possibility and impossible to define with current methods of understanding.
 
Register to hide this ad
This is not to say there's no value in current methods, testing or specifications. There's obviously tremendous value in it, and while it may not get us all the way there, it's the best we've got and gets us most of the way there. However, the takeaway is that no single piece of equipment can be seen, experienced, or taken in isolation from everything else, and if it is, it probably isn't going to portray as accurate or repeatable a picture (or scenario) from a universal perspective as we think it is. We listen through imperfect ears (not test equipment) and all the possible combinations of equipment and everything else combined makes all available outcomes on what is perceived and experienced almost limitless. In the end, it is the perception of sound through an imperfect hearing apparatus (some would say subjectivity) that we notice and experience more than all the available hard facts, objective evidence and data we do know. We may try and convince ourselves that we are hearing what we are supposed to, or are expecting based on the numbers, but we hear what we hear and it cannot be dictated or informed through "known" measurements taken in isolation from everything else.
 
onanysunday said:
One thing that has always eluded me is why is it so hard to entirely know how a piece of audio equipment will actually sound based off its specs alone (predictively speaking). If they're truly doing their job, we should be able to rely on them 100% of the time to the point of full predictability and repeatability in sound every time when choosing equipment. However, this is not what we have and this isn't the case.
Click to expand...

Speaking as a layman, I'd say it doesn't seem so surprising that specifications, which are based on measurable values, don't allow you to know everything about how a piece of equipment will sound, because that's based on subjective assessment, and cannot be directly measured. Even isolating the equipment so that your opinion isn't coloured by something related to the other equipment it's connected to seems like a complicated task to get right, and not one that every listener, myself included, is necessarily going to want to spend much time on.
 
I just tried to have chatgpt explain how an amplifier works in a way like it had too many drinks.

The funny thing is, the answer is alike one would expect from some real people, especially the "I want more bass" types (myself, I suggest go fishing)
:biggrin:


Kun je dit antwoord naar het engels vertalen

ChatGPT zei:​

Ohhh, an audio amplifier, yeah, that thing! It’s basically like a magic wand, but for sound, you know? You’ve got this tiny little whisper of a signal... like, “psst, hey?” And then the amplifier is like, “WHAT?! YOU SAID THIS?!” and makes it mega loud. BOOM! Suddenly, you hear everything like it’s a rock concert.

Inside it, there’s, uh... a box of magic, or no, no, electronics! The signal comes in – tiny as a mouse – and then there are transistors or tubes inside that go, “Come here, buddy, I’m gonna make you HUGE!” And then that little signal becomes, what’s it called... a BIG signal!

You need power, though, ‘cause without power, nothing happens. It’s like the amp needs to chug a couple of espressos before it can work. Without that energy? Just silence. But with that power? BAM, the sound goes from “peep” to “WOW!”

So, really, if you think about it, it’s just a party for sound. The signal comes in, all shy and quiet, and the amp’s like, “No, no, no, we’re partying tonight!” And then… yeah, it blasts out through the speakers. Done. Cheers!


:biggrin:
 
I haven't used ChatGpt. The reason I mention and point this out it is because it's an elephant in the room that deserves at least some acknowledgement or discussion in a much broader sense than we've given it credit for whenever we discuss any equipment's performance. It's something we all kinda know on some level, but don't ever get too in-depth about or are unsure the extent to which it is having an effect. But why? This helps to try and explain all of what that is or could be. It's always somewhat alluded to here and there, but never taken on directly for the totality of what it is or actually means and represents in real-world listening, which is all we truly have to judge anything by in a realistic way. It's easy for us to become too pre-occupied and over reliant on specs alone to tell us what we should be hearing.

To hear any piece of equipment in reality [besides some all-in-one unit in different acoustic listening spaces] it must be inter-connected with other pieces of equipment and placed in an environment which will effect "or color" the final outcome (or performance) of the original piece of equipment. I don't know if Audio Science Review (ASR) has ever fully acknowledged this, or what their answer to it might be -i.e. specs *while critically important in providing some nominal baseline* are also somewhat less important than we give them credit for because we can never listen to them in isolation and our ears are not test equipment. Remember, and for instance, people make purchasing decisions based off specs alone which is why this matters and is relevant. If we had anything better than the incomplete, known specs we measure and look for, I am sure we would use them, but we can't because they don't really exist or may never be able to be truly defined in any sort of accurate way. It's just something to consider and add to your repertoire of musical combinations and infinite possibilities regarding the way equipment sounds. Things are not always as cut and dry or black and white as we make them out to be. Life also occurs in the greyscale. We have to sit with a degree of uncertainty that we are looking to avoid instead of thinking we know all the answers. Perhaps, it is nothing more than a reminder for us all to remain humble in what we do know and open to the possibility of new inputs or other factors and information not yet defined that is impacting our experience.
 
It seems like the topic involves the complexity of Fourier transforms and combinatorial explosion. This is a fascinating issue in signal processing, where the combination of multiple frequencies can lead to an overwhelming number of calculations, especially in high-dimensional spaces. Have you encountered challenges in managing computational resources when applying Fourier analysis to large datasets? It's always interesting to hear how others optimize their workflows to balance precision with performance.
 
Yes, this is really a high level mathematical concept. I haven't approached it from the classical perspective of having undergone my own measurements and calculations where I've arrived at a point of increasing complexity that I could no longer answer. I've read about it and internalized what it means and how it relates to the ambiguity of sound in a more general sense. The math (if done correctly with all possible factors taken into account) leads to a point where there are so many branching possibilities that it is almost infinite and it becomes increasing difficult if not impossible to obtain a definitive answer. The "answer" in this sense is what does a piece of equipment sound like exactly? The takeaway is always that "it depends".
 
Describing what something sounds like and experiencing it are two completely different things. Fortunately, there is a strong correlation between measurement and what we experience listening. There will always be differences in perceived sound because no two people have the exact same set up and no two people experience the sound the same way. It doesn't matter. Humans are very flexible and get used to differences easily. Humans also convince themselves of things that aren't real very easily, hence the large market for audio snake oil.

There may be subtle differences in wines grown in different locations and different years, but in the end, it's all just fermented grape juice. To me one is not worth much more than another. The same applies to audio equipment. There may be subtle differences in performance and sound, but in the end if I can still enjoy the music, the subtle differences don't matter and are not usually worth the extra $.

That said, there are real differences in the way equipment is made, and I can appreciate such differences even if they don't contribute directly to way the the equipment sounds. Speakers stand out in a room and should look nice as well as sound "good". I can live with the way different speakers look, as long as they look nice, and I can live with different sound as long as they don't distort. There are some very expensive speakers that I would not want to have in my home because to me they don't look very good. I like circuit boards that are well designed and laid out. I like the use of quality parts that will help ensure reliable operation, even if they don't mean the device will sound any better.
 
Is anyone here (besides BmWr75 earlier and Tonoje's post immediately above) NOT posting GPT material?
 
Last edited:
Way back when before digital there was always a debate on how much band width we really needed beyond 20 to 20,000. Mac amps were 16 to 40,000 HZ +/- .1 db with less than 10% phase shift. Phase shift is just another way of expressing frequency response. 360 degrees is 3 db. Band width is +/- 3 db or a 6 db variation. Ampex suggested 5 times, but did that mean 10 to 50,000 HZ or 20 to 100,000 HZ. I have for gotten. Another thing was how much signal to noise ratio was needed. If you have two pieces of electronic with the same signal yo noise then when a signal passes through them you loose 6 db of ratio or gain 6 db more noise than you had before. So If you have a room with say with 24 db of noise in the midrange where the ear is most sensitive and you play your music with peaks of 104 db do you really need electronics with more than 80 or 86 or 92 db signal to noise depending where you are using separates or not. If you have 80 db signal to noise then your distortion has to be less than .01% or you can hear the distortion as noise. .001% requires a signal to noise of 100 db. But if you have a sound 15 to 30 db louder than another sound in a similar spectrum the louder sound is said to mask the quieter sound so you can't really make an intelligent decision as to whether you can identy the quiter sound or distortion. So that means most of the time you can't hear distortion less than 2 per cent if its in the same spectrum as the fundamental sound. So if frequency response defines rise time, signal to noise defines noise and distortion, what left is there to measure. HArmonic and IM distortion are just forms of noise so they can be described by signal to noise it seems. But how to separate the primary sound from the noise to be measred. Thats why we have THD and IM tests. The problem is the IM tests only describe what happens between two frequencies. What happens between 10 or 100 frequencies react with each other. Thats the kind of testing we really need I suggest.

I would take my dual trace 100 MHZ oscilloscope and plug the input to my scope and then sample the out put going to the speaker of the units under test. I would use a 700 HZ tone to calibrate the two channels with a gain of the test unit set about 40 db and line up to two wave forms so the looked identical then it the differential function to fine tune the adjustments so the difference became as close as possible to a straight line ever increasing the sensitivity of the display looking for differences between the two traces. Which be distortion between the input and out put. Then I would remove the 700 HZ calbration tone and insert music or pink noise. Some units under test did a great jon some not so great. I tried using pink noise but the results were almost just to hard for my mind to decide which unit was best. All I could do was look at the envelope of distorted noise and decide which units had the smallest height of the envelope of noise. I will say older tube units had the widest variations in performance. SS units the best especially as more time passed during the late 60's 70's and early 80's. Units using digital stages were horrible at first during the early 80's and early 90's.

The question is or was what I had seen correlate to what I heard. Most of the time I would say yes. But there are always exceptions to the rule. So my method wasn't perfect for sure. It was just my way of looking at things at the time. I would think with todays powerful computers the answers could be much more accurate and real numbers could be assigned to the changes as the signal went through each piece or groups of electronics. Then we would know the difference. Then how do we interpret that difference so we can eliminate it? Thats way beyond me today and was back then in the 60's and 70's.

It was just and idea I had on how to see the distortion electronics were adding to the sound we heard. It was the total distortion I was seeing. I didn't know what was frequency errors, noise or harmonic or intermodulation or time shifts, etc etc. Maybe If I had used different test frequency to calibrate the signals of input versus output I would have gotten better results. But I didn't.
 
Assuming you're not a chat bot, I'd point out that a dual trace scope does not sweep both traces at the same time- they alternate. You might get them to look the same on a steady tone, but you're looking at two different waveforms shifted in time. When you switch to music or noise they won't line up any more because the waveform is changing. When look at the difference between the two waveforms you're comparing apples to oranges and you'll see a difference that doesn't exist in real time.
 
It's part of the reason better specs don't always correlate to better sound even though we think they should and is why equipment with the best specs can just as easily sound dead and lifeless (which misses the point of having them -at least for me) because it's mostly static measurement based and isn't measuring all the things that matter dynamically in multi-dimensional space or have an influence on all possible sound parameters or ways of measuring sound we haven't come up with yet. There's more than meets the eye and are many complexities and interactions happening outside the piece of equipment itself, so even if all the possible factors (or inter-dependent relationships) within a piece of equipment's sound were known, it's still susceptible to all the other outside forces and interactions of which it is only a part of. I suppose I'm flattered? people think I'm an all-knowing chat bot or something, but am just a regular person that has been on AK here for many years now, long before any of that.

I guess you could say I've been obsessed with trying to figure out what makes equipment sound the way it does, through differing circuit topologies as well as the components and component materials used to implement those designs. This is just something else to consider along with those other concepts which helps explain why things sound the way they do. In the meanwhile, I'll continue to go through all my equipment and enhance them by making the component changes I've found which impact performance in positive ways that gets them closer to the way I wish they sounded out of the box. Ideally, I wish I could just rely on the numbers in the product specification to help me arrive at the perfect sounding piece of audio equipment, but I can't. For instance, choose a piece of equipment with the highest SINAD rating you can find and tell me it always correlates to the best, most realistic piece of equipment you've ever heard.
 
Last edited:
9a3b688e-477f-4d89-9c57-231388cef219.gif
 
As far as I'm concerned (today) this remains as equally relevant as ever and should be discussed and referenced more as a way to try and explain (or allude to) the unexplainable when arriving at a net result of something involving many unseen factors. Science is ever-evolving. It's easy to assume it currently explains everything unexplainable, but it still doesn't and can't due to an almost infinite amount of variables and possibilities not yet considered. Sure, it gives us some reliable baseline information -tests and measurements that are predictable. In that sense, what we have now is always true and correct -although technically incomplete when considering all combined aspects that may effect a final (heard) outcome. However, I'm sure there were scientists a hundred years ago who thought they knew everything and had a handle on a topic as the "authority" of the subject. Over time, many of the details of what they thought they knew has changed, been revised, or was tossed aside completely. I take this as a reminder to remain humble while keeping possibilities open to new or other information coming in not yet conceived while staying vigilant in current best methods and practices in what it is we know now or can prove to someone else.

As humans and the premier, dominant species on earth, we often overplay our hand thinking we're always correct or are infallible as a result of the system/ society that has coaxed and shaped us and our knowledge base into believing we already know everything there is to know from the best minds that currently exist or have ever existed. At some point however, the curse of the fourier (as it relates to audio) extends beyond test measurements (in a philosophical sense) and becomes an indictment of our infallible hubris as the dominant species on earth. For better or worse, it seems (to me at least) that intelligence, technology, and the mastering of "systems" are placed on a pedestal as the pinnacle of human advancement and achievement. Those with the best information or technology above others are held in high regard and emulated as truth. The moral of the story is that at best, we only know part of everything that affects anything and we need to occasionally be reminded of that to keep an open mind, prevent stagnation and to move the possibility of progress forward.
 
Last edited:
You must log in or register to reply here.
Back
Top Bottom