@mapman .... Considering 'all of the above'...*ah* Yeah...*L*
Contrasted to speaker cables, lifted or no, IC's, USBees', and the conduit that one trips over on it's way to the breaker box....X the $'s to determine such.... ;)
(Rude, but bare with....😏...) Audio gear and underwear have details in common.
It needs to be 'comfy' enough to forget, because if it isn't.....
Comes in all sorts of materials, colors, types.....boxers to g-strings....loud or subtle...
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That being said 15 years ago there we’re great sounding dacs Mark Levinson 31 , there were many Multibit ladder chips out there from Burr Brown , and Analog devices , even Phillips
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Benchmark dacs are terrible sounding, these make dogs go wild with their highly and I mean over the top analytical sound. I also had the Audio Resesrch Dac 1 way back which would sound pretty bad these days. When traveling for work 14 years ago, I had an external battery powered $750 dac hooked up to my iphone that sounded very good.
The question should have been, are there any current dacs that sound bad or are not an improvement over what you get in a non-audiophile cd player. I’d still take my dac in my older Sony cd/sacd player over a benchmark dac, and the Sony dac can’t hold a candle to the newer better dacs.
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@curiousjim
I wish you luck!
@jmrrobbie1
No but there are some reviews on youtube. If I recall, the highs are reputedly somewhat "lively". As soon as I saw that, I crossed it off my list. Not to say you wouldn't like it. FYI, Listen Up! is a Hegel dealer and they've offered returns on new Hegel gear in the past.
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@chervokas
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?
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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.
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@jmrrobbie1
I have a Hegel H390. As an integrated amp, it’s top notch, but like several other brands, they feel obligated to include an okay DAC and an almost useless streamer. I’m sure their new DAC is wonderful, but I for one would feel better about buying one if I didn’t already have something built in to the H390. For the same price range, Hegel is up against a bunch of other DAC’s!
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Audiogoners have become more civilized. Regarding the sound quality of the Benchmark DAC3, I recall making no negative comments myself. I simply referenced GoldenSound’s review, which also made no negative comments—just described it as ’fine.’ Let’s be honest, ’fine’ simply means ’not great’ but still ’good.’
Oh my god, you wouldn’t believe how much backlash I received from forum members who like the DAC.
But now, look at the numerous negative comments describing the Dac ’bad’ from so many people here—yet there’s no pushback from those who own / like the Dac.
The only explanation I can think of is that Audiogoners have become more civilized. But what caused such a cultural shift in such a short time? Very interesting. Honestly, I don’t believe that’s the case, and I think those who attacked me owe me a sincere apology.
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Yes. Topping sounds poor to me in the mid range, especially for women's voices. I find it harsh.
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I have the Topping E70Velvet and it sounds superb. I think everything is system and personal preference dependent. Plus, everyone assumes people's ears are all the same...not true.
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Today, it is expected that any dac over a $100 sound pretty decent with either improvements or a sound emphasis that perhaps provides a noticeable improvement or works better with one's amp, speakers, etc., that supports the increases in price.
A higher voltage output, better separation, a bit better tonality, more note weight, stage sizing on all axis, less distorted sounds, etc., etc., however minor differences to some are highly noticeable by others.
Functionality and capability also come into play. Build quality, Reliability.
Seems dacs these days have a lot to offer at nearly any price point.
But I remember the old TDA chips that Philips produced that could be so natural sounding, It was a budget chip that when properly implemented...it was nice. It may not have had the larger stage size or punch as some others, but it could give a more natural rendition.
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I use a modified and expanded Yamaha A3000 sampler I bought in 1997 as a DAC because it is simply the best sounding piece digital conversion kit I have ever heard... A sampler is after all; a DAC on steroids.
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There are some great resources that map subjective sound claims and terminology to specific frequency response characteristics:
 
It's worth considering that a low noise and distortion DAC with a flat response can always be DSPed to achieve the kind of distortions that are appealing to the listener. Badly measuring DACs are only appealing to a select few.
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@markwd
Interesting chart. Thank you.
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Charts like that are invaluable to help understand what we hear in music better and use tools like DSP to adjust the sound to personal preference.
Agree starting with a high quality neutral sounding DAC then tweak to one’s heart content from there is a very practical way to go.
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The original premise here was that all DAC's these days are "good". Yes tech has come a long way to get much more bang for the buck on the low end of DAC's. However, I still feel there are differences up the food chain. For instance, I personally prefer a R2R type DAC than ones all using the SABRE chip. Also, like "warmer" than more analytical. I also wonder if all DAC's are benefiting by being fed with better streamer devices etc. Back in the day, I fed my DAC off a lousy noisy laptop.
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I don't know .......I have a 12 year mytek dac I run my TV and streamer through. I disconnected the streamer as Youtube sounded just as good to me (use it like a radio). I have an Ayre CD SACD and DVD player (20 years old) sounds pretty good. In my other system I have a Wadia 921/922 with an Esoteric transport. (I've never heard digital better than this) admittedly I will play vinyl most of the time. That t said without the full commitment to the vinyl playback hobby, I think digital is a terrific alternative. I don't own any modern DACS. I'm generally satisfied with what I have. I haven't heard any streaming setups that got my attention yet. That needs be be addressed if anything can compete with what I currently have.
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Recently compared a Topping D50III ($250) to a HoloAudio May L2 ($5K). SLIGHT differences, where depending on music played I SLIGHTLY preferred one over the other. DACs linked in Roon, volume matched, both connected to preamp, so could switch source on preamp with click of the remote. Differences in musical recordings and personal tastes are more decisive than objective quality.
And yes, I selected the D50III based on excellent measurements and listening reviews on ASR. The May was chosen based on review by Goldenear who infamously debunked MQA.
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After reading his NYT interview, ask Chad Kassem if there are any good DACs out there.
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The biggest issue is not the chip, it is analog part. Cheap DACS use cheap op amps and electrolytics as well as do not isolate digital and analog power supplies.
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This is funny many will choose denafrips terminator because it’s really excellent DAC. When Trelja heard the whole line of Denafrips. He prefers the Ares, this probably 7 yrs ago. So I went to axpona and went to listen to terminator and Ares . Joe was right , the Ares sound bigger but many listeners loves the terminator.I bought the Ares demo.
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Bad? Good? Depends on what you're using as your reference.
Sure, any DAC should sound better than no DAC at all. But once you start listening to more DACs, you may decide, "Yeah, that DAC doesn't sound so great after all"
Fully agree though that DACs' have come a long way over the years
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@mikhailark I don’t disagree with you about the importance of the “analog part” or the power supply(ies). The question I have is this: assuming a modern high end DAC with sophisticated power supply and presumably much higher quality “analog parts”, like say a Mola Mola Tambaqui, and measures essentially the same as several hundred dollar Topping D50III, how can they sound different? Wouldn’t we expect all those great “analog parts” in the Mola Mola to not only affect the sound, but also affect the measurements? Are the measurements or are our ears wrong?
I purposely pick two devices at opposite ends of the cost spectrum to ask this question because any difference in perceived sound cannot be from some artifact or coloration that tricks us into believing it sounds more musical. Either the marketing and our biases related to value are coloring our judgement, or there is more to accurate and enjoyable sound reproduction than can currently be measured on the bench top.
This may be part of it. From an email exchange between Mola Mola’s Bruno Putzeys and Stereophile’s Herb Reichert regarding the design of the Tambaqui DAC:
"Initially, I looked at using only a single, high-current switch to convert the PWM signal, but it soon struck me that running a number of them in a time-staggered fashion would allow me to remove most of the PWM carrier right away and so reduce noise. That was the core of the design. The remainder of the project was being completely anal about all the other stages of the converter: digital filtering, clocking, and analogue-output filtering.
"Of those, only the digital filter needed to be optimized by ear. It’s pretty obvious that a more stable clock is more ideal, and an output filter with lower noise and distortion is also more ideal. But there’s no ideal upsampling filter, a priori: The ear is not a spectrum analyzer. You need to listen to original high-rez files, filter them down, upsample them again, and then hear which kind of filter chain leaves the smallest sonic fingerprint. That is to say, how do you get from high-rez to (eg) "Red Book" and back whilst getting the smallest possible audible change? And then it turns out that a lot of filters out there sound really impressive, but only because they’re heavily euphonic—not because they’re sonically neutral....To make matters worse, the optimum design differs for different sampling rates....”
So perhaps there are elements of sound reproduction related to filtering and signal reconstruction that are as much art as they are engineering and physics, and sometimes what sounds more natural to our ears - especially in reconstructing a 16/44.1 signal can’t be deciphered by measurements, or in some cases looks like errors or spurious information? But this is still in the realm of digital processing, and has little to do with the analog section.
Putzey’s email goes on to say:
"Clocking was addressed using a very stable, non-adjustable crystal oscillator—adjustable ones are quite noisy—and synchronizing the signal using a homegrown asynchronous sample-rate converter that forms part of the digital filter. How that was done is a story in its own right, but it might take us a bit far [afield]. Same for the analogue output filter stage, which is also rather original in its conception. So, as much as you’d like to know what the magic ingredient is, I can only tell you that it’s about getting all the parts right, not just individually but as a system. It’s not sexy, but then real engineering rarely is."
Also on the analog and power supply side of things, it is possible that a device with a cheap power supply is injecting noise into your system and reducing the overall performance. Why some people immediately replace wall warts typically found with less expensive electronics with more substantial linear supplies. Also why some of these less expensive device may perform well when measured in isolation, but sound less pleasant when placed in a high end system.
kn
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I’ve owned DACs since 2007, and overall, their sonic quality seems higher now. In other words, a rising tide (technological progress] generally raises all boats.
But I do hear significant differences between delta/sigma designs vs multibit and NOS (all 3 of my current DACs are NOS). As soon as I was exposed to my first non-d/s DAC, I heard these differences quite clearly.
I understand that NOS DACs (by and large) measure poorly compared to d/s. I'm not an audio designer and just don't care about that. Sound is all I care about.
To my ears, d/s designs tend to sound clinical and cold, edgy, while NOS never does. On the other hand, subjectivity being the essence of our hobby, it must be acknowledged that some people love the sound of clinical, cold edgy DACs.
All I can do is figure out what my sonic preferences are (audio experience buttressed by exposure to music IRL), then select component based on that.
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@knownothing - measures what exactly? Frequency response, noise and harmonics are only metrics of ONE frequency. My major was in signal processing and spectral analysis. 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.
Remember when equipment measured awesome but then someone discovered that some gear sounds better and that, apparently, signal slew rate is very important and not just sinewave with 0.00001% THD. A bit later people discovered "joy" of intermodulation and started measure transfer of 19 KHz + 20 KHz since it produces 1 KHz parasite. Ah, but there are so many frequency pairs like this. So you have minimized 19 and 20. But what about 18.7 and 19.95? Or triplets? Or quads? Or that white noise that includes all frequencies?
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@aberyclark
"I have the Topping E70Velvet and it sounds superb."
I am curious. How much opera do you listen to? How many Cds with sopranos do you have?
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@mikhailark Reviewers like Amir at ASR also include multitone tests to look at more extensive IMD phenomena:

In terms of music comparison, there is software like Delta Wave Null Comparator that can facilitate doing exactly that. To use with DACs, you have to confront that the ADC will have digitization limitations. For speakers and headphones, you have microphone/space considerations that are better accommodated using systems like Klippel that use repeated measurements to achieve anechoic approximations in regular spaces.
I recommend Audio Science Review as a resource for learning more about measurement techniques.
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@markwd - yeah, I am familiar with the guy. He is just hobbyist, some former Microsoft guy that made money on stock options and thinks he knows everything. Typical corporate VP buffoon. Multitone is OK, but still not enough.
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@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.
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@mikhailark Well, attacking him (inaccurately, nonetheless) doesn't actually demonstrate the validity of your claims. You will need to actually show that the limited precision of a given FFT measurement results in audible differences. You could also try out the Delta Wave system and see if you can use that as a path down the golden road towards enlightening us all!
You can also check out my presentation of the debunking of Fourier indeterminacy and related claims in fora here and at the Roon community. Personally, I have nothing invested in any of this, but I find it curious how assertive so many folks are about their limited knowledge. Epistemic humility is the cornerstone of scientific progress.
Please show!
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@markwd - I owe you NOTHING dear. You go to ASR and discuss "audible" with your buddies and test new awesome $100 DACs.
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@mikhailark But it would be totally awesome and change everything if you could prove what you are claiming! It would be sooooo cooooool. 
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@markwd Dude, all proofs are at ASR, you know everything. Everything is the same, measurements are everything. Go chat there.
https://www.sciencedirect.com/science/article/pii/S0263224123009363
The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies, amplitudes and phases; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics.
What else do you need to know about FFT being just an approximation? LMAO. Now you gonna tell me "but it is so small so it is not audible". Right?
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@mikhailark Sure, but you are shifting your arguments around concerning the validity of multitone measurements (you assert they are insufficient but do not demonstrate why) and now you are asserting that known limitations of frequency domain methods make those measurements unhelpful or unreliable or something. It's just unsupported and baldly argumentative.
It would be very cool, however, if you demonstrated that you can show something important about audio systems that goes beyond the measurement methodologies widely employed! Sooooooo cooooool! 
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@markwd - why do you think I care about your opinion?
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@mikhailark Because of all the rich commentary I bring to the discussion thread!
There's null testing via software analysis and the reminder that multitone measurements do rule out some of the ambiguity around the specter of single tone testing. There's my always helpful reminder that it is important to show rather than just telling and how that is a critical part of our modern technological society. There are my insights on philosophical ideas dating back to Socrates (at least).
But mainly so that others can pick up on these diverse opinions and insights and make good decisions about resources and ideas related to our shared love of music and the technology of music reproduction! Sooooo coooool! 
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@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.
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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.
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@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.
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@mapman lol - see what you started?
@chervokas excellent post(s). While I think you went quite far in explaining how different digital filters can be perceived and appreciated differently by different listeners, I am not sure you exactly answered my question regarding how DACs that currently measure “the same” on the bench can sound different to listeners. In other words, what is needed in terms of measurements to better approximate how a DAC, or really any piece of gear or cable, will sound to a range of listeners? It just feels like the field of how psychoacoustics interact with sound reproduction and measurement still has a ways to go. I have a head cold right now so maybe that is clouding how I am receiving what you have written (and my posts on thus thread for that matter). Apologies if I am not tracking.
kn
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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.
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.
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@deep_333 now there’s a conversation starter.
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It's like woody Allen Said about sex. "There are no bad one's only better"
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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
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