This is incorrect. No matter what your favorite color is, we can easily measure if something is blue or red or whatever. The truth doesn't care about subjective preferences.
In audio reproduction to get closer to the truth, you need to measure a reproduction system along with the actual performance it's reproducing.
The components/system that measure closest to the live performance, are/is the closest to the truth.
Whether or not people like how this system sounds is irrelevant.
A common reason for using a notch filter is to minimize added distortion from subsequent A/D conversion. Maybe one could make an inverse digital filter to reconstruct the the original waveform?
Not exactly, the perception of yellow, orange, or violet can be due to various spectral combinations. Otherwise RGB video couldn't work.
Again, not exactly. It depends on how we measure. Typical Measurements with an AP analyzer fail to give accurate time-domain characterization of transient events. It doesn't represent the whole truth of real music reproduction. It also doesn't work exactly the same way that the ear/brain system perceives sound. Why that is the case has been explained in a number of recent posts in this thread.
A spectrum analysis conducted with the intention to capture THD spectral distortion components cannot necessarily reveal all spectral distortion components present. The reason being that a mathematically perfect fundamental frequency output spectral component can contain a multiplicity of fundamental frequency components, each having non-linear gain and whereupon the shape still remains undistorted as fundamental frequencies. This is to suggest that there can exist any number of non-linear gain fundamentals, all having variant phase shift being gathered into a singularity.
THD measurements can be considered only valid as a figure of merit under circumstances an input sinusoidal stimulus never changes of amplitude. The conclusion is that notching out the fundamental, or considering the fundamental as an undistorted spectral component is questionable under circumstances of ultra variant input stimulus.
For devices having a non-linear transfer function the incremental gain is variant as related to the tangent at any point on the curve. Ultimately it is incremental gain variance that generates distortions as causing the spectral components from whatever input stimulus is present. Hence it may be better to observe the shape of the output non-linearity using a triangular or sawtooth input stimulus than observing output spectrum. This generates the question as how to superimpose a true sawtooth on top of the resultant shape and the mechanism that our hearing relates to such differences.
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Incremental gain is the value as variant from some reference gain. As an example if some reference gain is established being 10, the incremental gain as "tangent to the slope" of the reference gain can be 10.01. Hence the gain changes can be small.
Correct but a spectrometer returns a single value. An individual's perception of that value is a different subject.
Yup I agree. I glossed over the fact that our known/available measurements are inadequate. My point was that if you know and are able to measure all the pertinent info, then subjectivity has no bearing on facts/truth.
In my own reality and perception I may say that it's a mile to my nearest grocery store. An odometer however will show that fact is different.
Yes, incremental gain is the derivative of the transfer function. Also known as small-signal gain. It's not difficult to measure directly.
That doesn't matter as an amp or DAC has no relation or relevance to the ear/brain system. They are components with electrical signal processing duties, with no interface to humans, and the sole arbiter is how accurate it converts or replicates the input signal. Full stop.
If you just think shortly about what it would mean if it was the way you describe it, you will find that it is simply not reasonably that an amplifier had a notion of how the brain works in order to make a perfect amplification job....
By this it of course follows that neither can a measurement system that aims to characterise an amp or DAC, have (it shouldn't) insight into human brain functioning.
I think you must have misunderstood the duty of an AP - its not, as you write to "represent the whole truth of real music reproduction" - but to analyse electrical signals.
A measurement system has a certain accuracy with which it displays a DUT's performance - that can of course be questioned - please describe how more specifically you feel that the AP fail in this sense for e.g. transients as was mentioned.
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Yes, under average steady-state conditions after phase information has been discarded. That's not a complete signal analysis of a reproduction device. It potentially misses and or minimizes a lot, so its not necessarily 'the truth' with respect to how people actually hear. That was my point. This assumes we are interested in characterizing audio devices in a way that is relevant to their intended end use.
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Sure. Though my primary issue isn't with the small signal gain variance about any point of a non-linear transfer curve, rather that for large signal sinusoidal input stimulus the input to output gain of the fundamental frequency can be of non-linear gain for variant amplitudes of input stimulus. It is only under the special circumstance that the amplitude of the sinusoidal input stimulus is fixed that the gain variance of the fundamental frequency can be ignored. In other words the fundamental frequency can only be notched out or ignored as being inconsequential if the input signal never changes amplitude. This is to say that the total gain, as the summation of linear and non-linear gain of fundamentals, cannot be discriminated from a linear gain setting if the amplitude of the input signal doesn't change.
It is a common suggestion that psycho-acoustic phenomenon relates to the existence of 2nd and 3rd harmonic. As DC shifting and non-linear gain fundamentals are intrinsically connected with harmonics it is questioned if the non-harmonic spectral components can be dismissed of contribution to psycho-acoustic phenomenon, particularly if generated preceding a network such as an RIAA filter that magnifies those spectral components.
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Gain on a large signal will vary with amplitude because the transfer function is not a straight line. But gain on a large signal contains very little information. It is much more interesting to measure the small signal gain as a function of output voltage and current, over the whole voltage and current span, and plot its variations. It probably also depends on slew rate (esp. current slew rate) but I haven't found a convenient way of measuring that yet.
Your method seems interesting to me, even if honestly I was not able to follow it in all details (for my limitations). I think that the real challenge is, in addition to developing a relatively simple measurement procedure, that of obtaining the quantities of interest that can then be correlated more or less directly with the sensations of listening. Dealing with transient phenomena, frequency analysis shows many limitations: it is probably more effective to work in the time domain by analyzing what happens to the transients, trying to precisely synchronize the source and measured signals, perhaps inserting appropriate chirp signals.
Here's an example:
The circuit R1 D1 R2 has a gain of 1 if v(in)<0V and a gain of 0.5 if v(in)>0.6V, with a transition as the diode turns on. Its transfer function is on the left.
If I run a sinewave through this circuit, the top will be squished. But the harmonics plot is very unhelpful, and the THD residual is kind of useless. They don't help at all to determine what's happening. In fact it would be a lot quicker to look at the output signal on the scope.
Now...
If the transfer function is f(x), out=f(in)... on a complex circuit we can't measure it directly, because we'd have to use a ramp signal, and that is very sensitive to phase shifts. And we can't make the ramp slow enough to ignore phase shift, because we're interested in what happens over all audio frequencies, not just DC. We can use the zero crossing points of a sine wave as an ersatz of a ramp, but we'll have to sample very fast with lots of bit depth.
Its derivative f'(x)=dy/dx is more interesting anyway.
If we set the DC operating point to an input voltage x, we get an output voltage y=f(x). If we add a small signal dx to x, making it x+dx, then the output will be f(x+dx) which is approximated as f(x)+f'(x)dx... the incremental gain at the DC operating point x is the derivative of the transfer function.
So I replace dx with a low amplitude sinewave. If the DC operating point is set to x, then using a signal x+a.sin(wt) with small enough value of a, then the output will be f(x)+f'(x).a.sin(wt). Because x is constant, all we have to do is detect the amplitude of the small sine in the output, and that gives the incremental gain directly.
On a real amplifier it is not possible to use DC because transistors will heat up, that will upset the bias, and there are coupling caps. So instead of DC I use a low frequency high amplitude sine wave (20Hz), with a high frequency low amplitude sine wave on top. This test signal is on the top graph:
On the middle graph, after the circuit, the top half of the signal is squished. This applies equally to the LF and HF sine waves. Then, a highpass filter gets rid of the LF, leaving only the HF (bottom plot, blue), and the soundcard detects its amplitude, which is directly proportional to the incremental gain. It's obvious on the graph that this circuit has double the gain on one polarity of the sine. If the phase of this HF sine is also detected, then the phase shift of the circuit is measured too, at all bias points swept by the low frequency sine.
This works well because soundcards can measure the amplitude and phase of a sinewave with excellent accuracy.
@Markw4 you could do the same for DACs.
For a DAC it's easier because you can input a perfect digital triangle waveform. It should be very slow, much less than 1Hz, unless the DAC has a digital highpass filter... in this case it should be of a proper frequency to go through. So this will slowly sweep the DC value. Then add a very small sine wave, something like half a LSB of the sigma delta multibit DAC. So if it's an ESS with 6 bit DAC in the output, perhaps 1/64Fs to 1/256Fs. Then highpass to get rid of the slow signal, detect the amplitude and phase of the HF signal with the soundcard, and plot it versus the DC point. Ideally, it should not change at all... but does it?
I've done it for noise, using just a very low frequency sine, and the amount of noise in the DAC output does change versus the "DC" digital input level.
These tests require the DAC and ADC to be synchronized, especially to measure phase.
For a DAC it's easier because you can input a perfect digital triangle waveform. It should be very slow, much less than 1Hz, unless the DAC has a digital highpass filter... in this case it should be of a proper frequency to go through. So this will slowly sweep the DC value. Then add a very small sine wave, something like half a LSB of the sigma delta multibit DAC. So if it's an ESS with 6 bit DAC in the output, perhaps 1/64Fs to 1/256Fs. Then highpass to get rid of the slow signal, detect the amplitude and phase of the HF signal with the soundcard, and plot it versus the DC point. Ideally, it should not change at all... but does it?
I've done it for noise, using just a very low frequency sine, and the amount of noise in the DAC output does change versus the "DC" digital input level.
These tests require the DAC and ADC to be synchronized, especially to measure phase.
There is already a common test delta-sigma dac designers use which is to send the dac digital audio that consists of a DC offset. Noise is measured, then the DC offset is stepped to the next offset. By that means noise can be mapped out verses dac analog output signal level. The noise is produced by sigma-delta modulation is signal-correlated, including for a DC signal (although dithered modulators can be designed to help with that). The actual noise created by modulation is a good example of a complex signal other than what we commonly think of as noise (sometimes can be a whistling noise that rapidly sweeps across the audio band as a function of the audio signal), but it can look like noise on an FFT. @MarcelvdG has written some interesting info about it here in the forum.
There is another modulator noise mechanism described by ESS in which state-variable settling after loud transients followed by relative quiet sounds can produce an audible 'fssst' sound. ESS said they trained all but one of their executive team to hear it. The one guy who couldn't learn to hear it was Martin Mallinson.
MarcelvdG also described a low level 'whooshing' sound made by his chaotic modulator design during periods of silence. He said the volume had to be turned up to hear it.
There is another modulator noise mechanism described by ESS in which state-variable settling after loud transients followed by relative quiet sounds can produce an audible 'fssst' sound. ESS said they trained all but one of their executive team to hear it. The one guy who couldn't learn to hear it was Martin Mallinson.
MarcelvdG also described a low level 'whooshing' sound made by his chaotic modulator design during periods of silence. He said the volume had to be turned up to hear it.
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I would beg to differ. Looking at the time-domain residual is bascially looking at the sample value transfer function error directly, with only little deformation (at the top and bottom section of the exciting sine).
Only the observation of the development of the residual error vs level finally gave me the right clue what's really going on with the infamous "ESS hump"... a periodic ripple on top of the sample value transfer function. The total number of periods of that ripple correlated to the number levels of the final output DAC, bingo.
Staring at spectra doesn't give much insight, I would agree, though.
That was a great investigation! Did you find out if the ripple was due to HF noise modulation creating variable DC offset in the output opamp, or mismatch between the DAC output elements, or something else?