Is there any such thing as a bad sounding DAC these days?

FFT is a mathematical transformation from time to frequency domain. Our ears respond to frequencies over time. The details of how they do that is a whole different story.  chervokas  seems to have a good handle on it.

Not to derail the thread, but one of the cool things about our hearing that's different than a Fourier Transform is that, yes, we process the separate frequency components of the complex wave separately, but we process them at the same time that we process the timing, because, at least up to about 5kHz, the nerve impulses generated by the movement of the stereocilia are phase locked to the input wave,  so our hearing is simultaneously using information about which location on the basilar membrane/which hair cells/which neurons are being activated and also the phase locked/timing neural spike pattern of that activity. 

You might be surprised by hearing some very nice sounding DACs / players from long ago. They will absolutely measure like dog crap compared to modern. But our ear-brains do not process information via Fast Fourier Transform!

Perhaps surprisingly, our ears and brain DO process sound almost exactly like a Fast Fourier Transform.

Our cochlea and our auditory cortex are tonotopic.  When a complex wave gets to our inner ear, different frequencies within the complex wave have peak resonant points at different physical locations along the basilar membranes of our cochlea which have different stereocilia bundles connected to them. Our inner ear actually breaks down the complex wave into component frequencies based on where each component frequency maximally excites the basilar membrane, and we have separate nerve firings for each of those component frequencies based on the hair cell bundles connected to the basilar membrane at those locations. The tonotopic geography continues into the auditory cortex in the brain, which Dr. Nina Kraus of Northwestern likens to a piano, where you see different physical regions in the auditory cortex responding to different frequency components of the complex waveform.

So, yeah, actually, our ears and our brains are breaking down incoming complex waveforms into their component frequencies very much like an FFT, and, further, actually converting them into binary-like neural spikes -- when a stereocilia bundle is deflected it creates a nerve spike or no spike, functionally like a 1 or a 0 -- and those go up to higher centers of our brains where the physical separation continues until other processes take place to create a perception of an integrated sound (or multiple separate sounds).

It's a sidebar to matter of what people prefer in terms of the particular sound of a particular piece of equipment. But our ears and are brains, when we hear, are very much doing something very like an FFT.

So, if I’m reading you correctly you are saying that our brains re-convert (analog) sound waves into digital?

It’s not really digital, though Susan Rogers, who was Prince’s recording engineer then went on to get a PhD in music cognition and psychoacoustics and now is the director of the Berklee Music Perception and Cognition Laboratory, quaintly does describe our stereocilia as the inner ear’s little A to D converters. There are aspects of our hearing and our auditory processing that are like analog audio signal processing, and aspects that are like digital audio signal processing. Better to say that our ears convert mechanical motion into nerve impulses and those nerve impulse are generated when little channels open and let ions flood in, and those channels are either open or closed, and that train of either/or electrochemical impulses are the stuff the higher order areas of our brain uses to form a perception of the sound -- Psychoacoustics: Hair Cells in Ears are Analog-to-Digital Converters | Susan Rogers | Berklee Online

Absolutely fascinating!!  Any penny that bright can get thrown on the tracks can't happen often enough.  Do you mind sharing your background to have that knowledge?

I'm just a guy who is really interested in how stuff works, and that includes the science of perception. You know, we live in this hobby with this objectivist/subjectivist battle sort of bequeathed to us 60 years ago by J. Gordon Holt and Julian Hirsch et al., but our ability to measure sound, and especially our understanding of the science of perception have changed so much in 60 years, it's kind of mooted that whole divide for me.  I read Daniel Levitan's book This Is Your Brain on Music when it was published in 2007, but I really didn't start reading in the science of hearing and psychoacoustics until after watching an episode of Nova called Perception Deception, and realizing how far the science had come and how little I knew about it (in fact, when they teach the general basics of how hearing works to people, it's so oversimplified that most of us, and certainly I previously, have a faulty understanding of it).  

I've also been a musician for most of my 61 years and done a bunch of audio production work, so I knew how to make sounds, yet it seemed like I understood very little of the "last mile" of sound -- hearing and auditory perception.  So, I've just been learning it a little bit, through reading Brian Moore's classic primer, An Introduction to the Psychology of Hearing, through reading some of the work of and listening to lectures by the likes of Stephen McAdams, Nina Kraus, Susan Rogers.  I'm just barely a beginner in the subject, but I've learned enough already to realize there are a lot of common misconceptions and widely held partial understandings. 

For example, does anyone measure equipment using white or pink noise (better representation of actual music) and compares spectrum? Or, better still, take a piece of music, play back via two DACs, then measure difference in analog outputs using high precision instruments? Never seen any measurements. So there.

Well, null tests are common enough with music signal, loop back testing too. And noise is used in testing things like DAC filter performance. Noise as a test signal is common enough in addition to both individual frequency testing and frequency sweep testing (which is going to be better at showing you the spectrum of harmonic distortion than what you'll be able to glean from noise).  Noise is challenging for some of these tests -- like you can't can't measure SNR with noise obviously, with DAC if you have random noise like white noise you can wind up with randomly occuring overs, I guess.  And of course it's really not so much a signal more like music, I mean, music doesn't have anything like random frequency and constant sound power across all frequencies, unless you're listening to something like Merzbow or something. 

@knownothing 

Bruno Putzey is obviously a brilliant circuit designer, but he’s not quite right when he says "the ear is not a spectrum analyzer." Maybe he hasn’t looked into hearing and auditory perception as much as he’s looked into circuit design.

When a complex wave -- like the sound of music -- reaches our cochlea (in the form of waves in a viscous fluid propagate down the cochlea), different frequency components of that complex wave maximally vibrate different physical locations along the basilar membrane running through the cochlea, attached to those specific points of the basilar membrane are inner ear hair cells that fire in response to that particular frequency component because it is that component that moves them. Additionally, the nerve firing driven by the hair cells is phase locked to the signal (at least for signals below 5kHz) -- the nerves fire at the same point in the frequency’s wave over and over.

So in fact, our ears take an incoming complex signal, break it down into component frequency parts, track the frequency both via the timing of its cycle and the degree of BM displacement, and our brains do comparisons of the data to make determinations about how to perceive the sound.... we compare interaural time and level differences, and phase differences of the sounds as they reflect off our left and right pinnae to assign location; we decide which components should be heard together as a fused tone with a timbre and which tones don’t belong to that and so are heard as something separate (we use lots of info for that including learned knowledge of what X instrument sounds like, what sound components start and stop more or less together, what sound components are behaving continuously and which ones are discontinuous with those, the location of each of these individual components, etc.)

The ear and brain work very much by breaking down a complex sound pressure wave into component parts and analyzing them. It just then goes a step further and concocts and auditory perception out of the data it collects, and that is what we hear.

There actually is another explanation -- not just unconscious bias or difference in the stimulus -- for differences of people’s experience listening to the same equipment. Frequency following response studies -- in which electrodes on the skull of people track the brain activity of people doing normal listening to sounds (and the electrical signal they output, remarkably can be played back and resembles the original sound) -- show that even for individuals with clinically normal brains and ears, each person has an individually different FFRs to the same stimulus, and the differences remain consistent for each individual relative to others over time. Our brains each actually are "hearing" something slightly different.

We also know from FFR studies and other kinds of studies that, for example, speakers of tonal languages have different FFR pitch consistency responses than speakers of non tonal languages; that the descending auditory pathway (which sends brain signals too the inner ear and seems to play a role in the active gain control and frequency selectivity of the ear’s outer hair cells) functions a little differently in trained musicians than non-musicians; heck, we even know that FFR pitch stability (having the same FFR response over and over to the same pitch) is worse in children growing up in poverty with poorly educated parents -- that is, science shows that for the same stimulus, individuals have different brain responses and that while some of those responses are biomechanical (women on average have smaller cochlea than men, making their basilar membranes stiffer and giving them gender average differences in hearing response than men), many involve things that are learned and conditioned or are behavioral (differences in attentive hearing vs inattentive hearing).

That’s all before we get to biasing factors like knowing X costs 3 times more than Y, or the impact of other senses, like sight, on auditory perception, which also have very real and substantial impacts. And then too before we get to how we develop cognitive models for preference.

What sounds "natural" to any one of us in something that we know is not natural -- a recording -- is a complex psychoacoustic construction that a measurement of the stimulus alone can’t explain, but which also many not correspond to another person’s psychoacoustic construction of "natural sounding" or even another person’s auditory experience as track by differences in brain activity through FFR.

So, to bring it back to D/S digital reconstruction filters, a lot of people prefer, say, a minimum phase reconstruction filter in a D/S DAC, some people might like these megatap filters, some people like an apodizing filters, some people might even like a sharp linear phase filter right at Nyquist (many people might not even be able to perceive a difference), and we absolutely can known and measure the response of each of those filters, and design them accordingly (you can play around with them yourself if you like with something like HQ player feeding a NOS DAC). What we can’t measure, at least not directly, is individual preference or average general preference. We need to measure those things indirectly through controlled, single variable listening with a variety of test subjects representing the whole range of listeners to have any kind of sense of those things.

It’s not that we can’t measure the sound -- and I don’t think Bruno is saying we can’t measure the filters, just that what he and his team think sound best aren’t necessarily the classically idea filters. It’s not that inexplicable magic is required. Its that people hear and are sensitive to different things in a given sound, leaving product developers with choices to make: do you make something that measures correctly, to you make something that sounds good to you, or do you make something that sounds good to most people according to studies and focus group data about group preference?

Fortunately, most of the time, things line up -- people on average in lab tests seem to have a preference for full flat frequency response and low distortion in speakers, but even speakers these days are commonly built not for flat anechoic response but to comport with a predict preference curve combining on and off axis response build on Floyd Toole’s research. It’s euphonic, it’s not accurate, but it is measurable and being designed for not just through accident or trial and error.

In this hobby there are obviously disparities in preference, in ideas of what fake things sound "natural," just like there are disparities in the music we listen to, in the type and quality of the recordings we listen to, and definitely in our home listening acoustic set ups.

I really don’t think it’s a matter of the bench tests and other kind of tests missing information that relevant to the sound the equipment is producing. I think it’s just that auditory perception and sound preferences vary among individuals.

@chervokas - to be entirely correct, it is just Fourier Transform (FT). FFT is a Fast Fourier Transform which is an algorithm (one of many) that implements FT in discrete form for a typical computer chip. FFT is only approximation, it is NEVER precise as Fourier sequence is infinite for complex signals like music. Thus, ANY transfer to frequency domain and back (such as for Dirac) is somewhat lossy. Discrete chips and methods all have limited precision.

I’m just noting that our hearing in fact does work in some ways that are analogous to a FT, in that our ears and brains break down an incoming complex wave into it’s component discrete frequencies. Our ears and brains don’t seem to have to flip between frequency and time domains, so that's a substantial difference in kind, we seem to be able to process both simultaneously by processing information from the location on the cochlea that is activated and the timing pattern of the neural firing so activated -- at least up to about 4kHz or 5 kHz above which our neural ability to phase lock to the signal breaks down, our perception of pitch starts to break down, and our ability to resolve timing with respect to frequency becomes less precise and depends on information we can glean from other biological processes.

But like anything else, our ears and brains are definitely far from infinite in resolution, highly non-linear even in the frequencies and spls and time increments that we can resolve, and limited in precision too.

A lotta bullsh here and in the previous post, are you recruiting chat gpt for the word salad as well?....there’s no frequency domain analyses, none, happening in human perception/auditory/cns.

Some crappy design/analysis tool never fit in your ear. Keep the human out of it and crunch away.

This is totally wrong. But I’m not sure how much reading or study you’ve done in auditory perception, hearing, psychoacoustics, etcs. I recommend Brian Moore’s standard text, An Introduction to the Psychology of Hearing, for a more layman’s but incomplete look, maybe Nina Kraus’ Of Sound Mind. Susan Rogers has some overly simplified but may more understandable videos at Berklee like this one, which is only slightly on the topic of cochlear tonotopicity -- https://www.youtube.com/watch?v=A83gc7qnCPI Honestly, I think you need to study up on hearing, auditory perception, the function of the descending auditory pathway not just the ascending one.

In psychoacoustics they model the cochlear function as it splits of the sounds as a series of audiotory filters, though that's just a way of talking about the functioning -- https://www.youtube.com/watch?v=KZj1YjwJ7sE

Btw if anyone cares, this is a reasonably simple explanation of how the ear ans brain separate incoming frequencies and map them to separate places in the braind -- https://www.augusta.edu/mcg/discovery/bbdi/neuroscience-of-hearing/6-12.php

And this is a pretty good look at how the active amplification and frequency selecttivity in the ear/brain system works -- https://pmc.ncbi.nlm.nih.gov/articles/PMC2888317/