tuga
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For reference, a recording of Berlioz' Lélio Op.14b by the hr-Sinfonieorchester Frankfurt & Eliahu Inbal (Denon 1989):
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Audibility thresholds of amp and DAC measurements
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tvrgeek
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I will soon have on hand my old Muse Wolfson first generation, Schiit Asgard AKM, and a Topping D30 quad Cirrus. I will verify them to the limits of my bench ( good enough to measure the Muse, but Schiit and Topping should show zip)
I will then compare them to the select tracts I can easily find brashness on and see which not only I, but my super sensitive wife prefers.
I can level match to a 1K tone through speakers. I also have my old Grados that seem to be revealing of faults. Good monitors, bad for listening and my even older Yamaha's which are delightful for listening.
Basically a .03, .003 and .0003% orders of magnitude if just looking at HD
I will then compare them to the select tracts I can easily find brashness on and see which not only I, but my super sensitive wife prefers.
I can level match to a 1K tone through speakers. I also have my old Grados that seem to be revealing of faults. Good monitors, bad for listening and my even older Yamaha's which are delightful for listening.
Basically a .03, .003 and .0003% orders of magnitude if just looking at HD
Yes, I listen to music in my living room and there are always noises even though mostly at very low levels. Street noise from outside, hum of the fridge nearby, louder sound of Air Con when its on, etc. For such an environment, I just wonder at what level does further improvement in SINAD become useless for my listening. It must be lower than 120.
are these SNR measurments at 50mv ?
or it's just the maximum SNR that this device can output ?
Max
DualTriode
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After 28 pages @Spocko nails it best.
In the world of SINAD what is easiest for me to hear and what interrupts the enjoyment of the music is noise. In terms of the electronics; hum, buzz, power line harmonics and hiss are the worst. These are easily measured.
You all can argue about how much Harmonic Distortion and IMD distortion is auditable all you like. After a point it does not matter. If the SINAD is better than 80-85dB you are not going even start to hear it.
If we are talking and measuring powered speakers the electronics SINAD will not ever be mentioned or even measured.
If when you sit down to listen to the music you can not hear it do not worry about.
If you can hear it carry it to the bench and measure it. What you hear will be way above the measurement threshold.
If you want to push the measurements, hook the speaker(s) to the electronics. Set up your analyzer and laboratory grade measurement microphones and measure the room, room noise. Run the analyzer sweep without the amplifier turned on. Note the level of recorded sounds; test frequency and harmonics. It will surprise you that the test software will confuse room noise for test frequency and distortion Harmonics.
Turn on the amplifier and run the same test sweep (chirp) with sound coming from the test speakers.
I have done the mentioned tests with the APx555 analyzer, APx500 software with acoustic measurement add on's and GRAS Laboratory microphones in a room with an assortment of amplifiers; Benchmark, Topping, Nad and Crown. They all sound the same.
Thanks DT
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Several writers on this thread already alluded to the fact that distortions along the sound reproduction chain "stack up". Sometimes in simple ways, e.g. like several white noise generators do. Sometimes in much more complicated ways. An otherwise insignificant distortion in one element of the chain may push the stack of distortions as a whole over the audibility threshold.
Another factor to consider is the fact that most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes. Changes in amplitude of 5% from one sinusoid cycle to another are quite common. A sinusoid abruptly going from zero to its max in half of its cycle are common in acoustic music and in not overly processed mixes of other genres.
And the third factor is non-linearity of human hearing system itself. It serves as a sound reproduction chain element with a significant added distortion, especially at low and high sound levels. The nature and level of added distortions varies among humans, as well as with particular human's age, health condition, level of oxygen and certain essential nutrients in his or her blood, degree of fatigue, and so on.
Consequently, what is traditionally considered "low enough" THD, or "high enough" SINAD may or may not be in fact sufficient for a particular listener striving to enjoy a particular piece of music. Moreover, the quantifiable measures pertinent to one sinusoid (THD), or a set of stable sinusoids (SINAD) may not be as applicable to a particular real life music fragment, which is neither singular nor stable in its harmonic representation.
So, if you happen to assemble a sound reproduction chain that is sonically transparent for you on all the genres of music you listen to, be happy with it, and here I agree with those saying that overpaying for replacing the chain components with exotics makes no sense at this point. If, however, the chain is not yet transparent to you on some music fragments, small reductions in distortions along the chain may be worth paying for.
Another factor to consider is the fact that most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes. Changes in amplitude of 5% from one sinusoid cycle to another are quite common. A sinusoid abruptly going from zero to its max in half of its cycle are common in acoustic music and in not overly processed mixes of other genres.
And the third factor is non-linearity of human hearing system itself. It serves as a sound reproduction chain element with a significant added distortion, especially at low and high sound levels. The nature and level of added distortions varies among humans, as well as with particular human's age, health condition, level of oxygen and certain essential nutrients in his or her blood, degree of fatigue, and so on.
Consequently, what is traditionally considered "low enough" THD, or "high enough" SINAD may or may not be in fact sufficient for a particular listener striving to enjoy a particular piece of music. Moreover, the quantifiable measures pertinent to one sinusoid (THD), or a set of stable sinusoids (SINAD) may not be as applicable to a particular real life music fragment, which is neither singular nor stable in its harmonic representation.
So, if you happen to assemble a sound reproduction chain that is sonically transparent for you on all the genres of music you listen to, be happy with it, and here I agree with those saying that overpaying for replacing the chain components with exotics makes no sense at this point. If, however, the chain is not yet transparent to you on some music fragments, small reductions in distortions along the chain may be worth paying for.
Oh dear, what you don't realize is that such 'changing amplitudes' are exactly created by more sinusoids. Something starting in a half-cycle is simply not a SINGLE sine wave, either. This part of your argument is simply wrong and confusing the issues. You can take any real signal and model it with a variety of sine and cosine waves of constant amplitude. That may sound odd, but it's entirely true.
Any sine wave that's changing amplitude does not have only ONE frequency present. There is a sum of sines creating such a waveform.
As to "sonic transparency" inside of a two channel signal, that is pretty much impossible, for reasons entirely outside the "reproduction chain",rather to do with the actual infomrmation present in an original soundfield.
https://en.wikipedia.org/wiki/Fourier_analysis
"general functions may be represented or approximated by sums of simpler trigonometric functions"
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DualTriode
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I have the impression that you are grasping at straw.
Put your waveform generator on the bench and create the magical waveform you are talking about.
Take that wave form that you have invented and play it through the amplifier connected to a test resistor. Test the result with your O’scope or analyzer. The test waveform will pass through the electronics untouched.
The bulk of the potential distortion comes from the speakers in your system.
In fact Linkwitz did a lot of testing of speaker distortion with impulse waveforms. Take a look at https://www.linkwitzlab.com .
Thanks DT
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Importantly, the DFT is a pure linear transform, and can represent any non-infinite input.
One problem here is that one can create a number of such models. For instance, by changing sampling rate and transformation window width. Or, in mathematical terms, by switching the orthogonal base of functions over which the linear transform operates.
This is a trivial fact actually. Analogous to the fact that number 42 can be represented as or 8 * 5 + 2, or 10 * 4 + 2, or 16 * 2 + 10, and so on.
Which brings us to another problem: the way an analog signal is represented in a particular element of audio delivery chain, and the way it is represented in human hearing system, can be quite different. Correspondingly, what appears to be a small distortion in the context of one representation can be a large one in the context of another.
And yet another problem is this: the Fourier analysis only works accurately for idealized Linear Time-Invariant Systems (LTS). Human hearing system is neither linear not time-invariant. Thus, formally, the LTS Theory doesn't apply to it.
In the context of LTS Theory, yes. In the context of mammal cochlea, not necessarily. The cochlea simply doesn't behave as a Fourier transformer. Far from it. Once again, it is neither linear nor time-invariant. It is highly non-linear in both frequency and amplitude. And its behavior at any given moment may drastically depend on the prior history of the signal.
What I meant is a system, which, for a particular listener who doesn't move his or her head while being located at a certain position, is capable of reproducing a recording in a way indistinguishable from real-life sound. Such systems exist. For instance, I built one last year for recording my daughter's acappella group. I honestly can't tell the difference if I don't move my head.
Anecdotal evidence abounds too. For instance, with "grand piano behind the curtain" prank practiced during some audio shows, highlighting lifelike qualities of a particular sound reproduction system. Usually it is exotic and very expensive, yet something like studio master playing through a well-maintained midfield ATC monitors can do it too.
Yes, I agree that distortions in a decently-priced low-power electronics (e.g. DACs) are all but sorted out by now. Mainstream high-power electronic devices (e.g. amplifiers) are still dicey: you'd need to spend significantly more to buy something well-behaved on a variety of music genres. As to the speakers and headhones, most of them, even supposedly professional or audiophile ones, are still distorting wildly. I believe we agree on all of the above.
What we still disagree on is the absolute suitability of testing the gear using artificially constructed signals vs testing using real music. This is not my idea: some researchers and engineers long proposed testing audio chains on a set of music fragments, comparing calibrated recordings of real-life performances with recordings of the representations of such performances through the audio chain. Simple metrics such as a smoothed and peak integrals per unit of time over squared signals delta were proposed.
This is all pointless. There are an infinite number of potential basis sets. None of this defeats your rather odd statement about "not made of continuous sine waves" since INCONTROVERTABLY BY YOUR COMMENT QUOTED HERE INDEED it is true that ANY REAL, FINITE SIGNAL CAN BE DECOMPOSED INTO A SET OF SINE WAVES.
You suggested it wasn't possible, but you just proved it was. Goodness.
captainbeefheart
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That argument pops up far too often, it's an old standby argument for the believers.
"We don't listen to sine waves, music signals are much more complex"
To be fair it is higher math and not generally taught in high school unless you are in advanced classes which let's be honest here, the folks that took these classes moved on to higher education anyway. Or some people really like math and learned it on their own, that's fine also it greatly helps understand complex concepts. It goes back to the age old question, is math something we discovered or is math a human construct to help better understand the world around us? It doesn't matter, math rules
Regardless of the math, one can just empirically work it out by viewing an oscilloscope. First look at a singular sine wave, then look at a piece of music you like through the scope, play with the time divisions here. Finally go back to a single sine wave, then add another, and another and another and another, you will start to see a pattern that the more sine waves you add the more the shape of the original sine wave changes to something much more complex and starts to look like the music file you played through the oscilloscope.
So yes we do listen to sine waves, and conversely any complex waveform you can imagine is nothing more than the sum of multiple sine waves of different frequencies.
"We don't listen to sine waves, music signals are much more complex"
To be fair it is higher math and not generally taught in high school unless you are in advanced classes which let's be honest here, the folks that took these classes moved on to higher education anyway. Or some people really like math and learned it on their own, that's fine also it greatly helps understand complex concepts. It goes back to the age old question, is math something we discovered or is math a human construct to help better understand the world around us? It doesn't matter, math rules
Regardless of the math, one can just empirically work it out by viewing an oscilloscope. First look at a singular sine wave, then look at a piece of music you like through the scope, play with the time divisions here. Finally go back to a single sine wave, then add another, and another and another and another, you will start to see a pattern that the more sine waves you add the more the shape of the original sine wave changes to something much more complex and starts to look like the music file you played through the oscilloscope.
So yes we do listen to sine waves, and conversely any complex waveform you can imagine is nothing more than the sum of multiple sine waves of different frequencies.
I literally wrote "most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes".
If mammalian cochlea behaved like a Fourier transformer operating in bursts of constant duration, it could indeed represent any signal as a deterministic set of sine waves with certain starting phases and constant amplitudes. But cochlea doesn't behave that way.
For instance, an amplitude-modulated signal of frequency f0, in the context of Fourier transform, can be neatly represented as a sum of two sinusoids of frequencies f0-f1 and f0+f1, f1 being the modulating frequency.
In cochlea, up to a certain threshold of frequencies difference, such signal would be still firmly represented as f0, with amplitude jumping up and down in discrete steps. With increase of the modulating frequency, cochlea may vaguely register the f0+f1 frequency, yet may stay oblivious to the f0-f1 frequency.
So, for a music fragment that is a sum of long-running perfect sinusoids with unchanging amplitudes, the behavior of Fourier transformer and mammal cochlea are somewhat similar. Once the amplitudes are changing more rapidly, and the components frequencies slide, appear, and disappear, the analogy breaks down.
The underlying fundamental mathematical difference is that Fourier transform is an integral transform, taking into account the signal behavior over the whole transformation window. Cochlea, on the other hand, is a rather limited electro-mechanical device, which lacks the capacity to do such linear integral transform.
Moreover, the Fourier transform is based on perfectly captured samples. In general, it is not robust in the presence of noise and missing information - there are theorems proving this. Cochlea doesn't capture the signal shape perfectly. In fact, it heavily compresses the information inherent in the signal.
So, even if the higher audio information processing centers of the mammalian brain could do the integral transform, they'd be lacking the data for doing so. Instead, the human hearing system does its own transform, which is highly nonlinear, behaves very differently from the Fourier transform, and is governed by parameters which may differ greatly from one listener to another.
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