AndreYew
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Just as important as measurements is the interpretation of the results of measurements. Anyone can measure stuff. Whether you can tell anything useful from it is another matter altogether. Jason's multitone test is a great example of that. It may not be everyone's cup of tea, but it obviously yields information that J&crew know how to read to find issues in their circuit. Linkwitz uses a shaped sine wave to characterize his speakers, whereas most of the rest of the world uses only impulse response. Measurements are just tools: how you use them is just as important.
As for multitone tests, the perceptual audio guys have been using it for a while to look at MP3 coders and similar things. These things do nasty damage to multitone tests, and sometimes that's audible.
THD, IMD, multitone, and other distortion measurements are all measuring the same underlying phenomenon: the nonlinearity of the circuit. Here linearity is rigorously defined, and it's what we all learned in high school algebra. A function is linear iff:
1. f(x) + f(y) = f(x+y) You can take two separate signals, add them, and the audio device will output the same thing as when it separately processes each of them and you added that together.
2. f(a*x) = a*f(x). If you make the signal bigger by a constant factor a, the output will also be a constant factor a bigger
That's it. That is all linear means. Here is a straight wire:
f(x) = x (what goes in comes out unchanged)
Here's an amplifier:
f(x) = a*x (the output is bigger by a factor of a)
Consider a non-linear function:
f(x) = x*x
This is not linear because:
1. f(a) + f(b) = a*a + b*b, which is not the same as f(a+b) = a*a + 2*a*b + b*b
If a and b are sine waves, and you apply some trigonometric identities, you find out that you get 2nd order distortion. Basically, if you have a transfer function that is a power series, each power is a higher order distortion. f(x) = x*x*x would have 3rd order distortion.
All multitone tests are doing is f(a+b+c+d+ ...) where a, b, c, d, etc. are the individual tones. If we get individual tones back out, then we know it's linear. If we get grass and fuzz and extra tones, then it's not linear. How non-linear depends on what extra crap comes out.
The problem with THD is that it wraps all of this under 1 number. You could have distortion components so close to the main tone that it's effectively masked out and inaudible, but that might generate the same THD number as a tone that's far away from its fundamental, and therefore way more audible. Some audio people have proposed an error signal measurement where you subtract the output from the input and look at its spectrum (basically --- it's more complicated).
One more interesting thing about this that a poster alluded to up above. Distortion combines in nasty ways, which is maybe one reason (I'm speculating) the awful performance of speakers and headphones are more tolerable than bad electronic distortion.
Consider this: your preamp is non-linear like this:
f(x) = x + a*x*x (a is a constant, and very small in very low-distortion devices)
It will have supposedly pleasant-sounding 2nd order distortion.
Your amp is also a bit non-linear in the 2nd order distortion way:
g(x) = x + b*x*x (b is another constant similar to a)
What happens when you play music through this system?
s(x) = g(f(x))
Working through all the math, you get:
s(x) = x + b*x*x + 2*a*b*x*x*x + a*a*b*x*x*x*x
Basically, you get extra 2nd, 3rd, and 4th order components presented to your loudspeaker. Your loudspeaker then adds its own specialness and produces even more distortion components.
And this is just non-linearity, and just the tip of the iceberg of what could go wrong. There are lots of other things, and they tend to be specific to the domain of the device in which they occur, eg. resonances in speakers, software bugs in DACs, etc., all of which can show up in these measurements, but may be very difficult to trace back to the root cause.
As for multitone tests, the perceptual audio guys have been using it for a while to look at MP3 coders and similar things. These things do nasty damage to multitone tests, and sometimes that's audible.
THD, IMD, multitone, and other distortion measurements are all measuring the same underlying phenomenon: the nonlinearity of the circuit. Here linearity is rigorously defined, and it's what we all learned in high school algebra. A function is linear iff:
1. f(x) + f(y) = f(x+y) You can take two separate signals, add them, and the audio device will output the same thing as when it separately processes each of them and you added that together.
2. f(a*x) = a*f(x). If you make the signal bigger by a constant factor a, the output will also be a constant factor a bigger
That's it. That is all linear means. Here is a straight wire:
f(x) = x (what goes in comes out unchanged)
Here's an amplifier:
f(x) = a*x (the output is bigger by a factor of a)
Consider a non-linear function:
f(x) = x*x
This is not linear because:
1. f(a) + f(b) = a*a + b*b, which is not the same as f(a+b) = a*a + 2*a*b + b*b
If a and b are sine waves, and you apply some trigonometric identities, you find out that you get 2nd order distortion. Basically, if you have a transfer function that is a power series, each power is a higher order distortion. f(x) = x*x*x would have 3rd order distortion.
All multitone tests are doing is f(a+b+c+d+ ...) where a, b, c, d, etc. are the individual tones. If we get individual tones back out, then we know it's linear. If we get grass and fuzz and extra tones, then it's not linear. How non-linear depends on what extra crap comes out.
The problem with THD is that it wraps all of this under 1 number. You could have distortion components so close to the main tone that it's effectively masked out and inaudible, but that might generate the same THD number as a tone that's far away from its fundamental, and therefore way more audible. Some audio people have proposed an error signal measurement where you subtract the output from the input and look at its spectrum (basically --- it's more complicated).
One more interesting thing about this that a poster alluded to up above. Distortion combines in nasty ways, which is maybe one reason (I'm speculating) the awful performance of speakers and headphones are more tolerable than bad electronic distortion.
Consider this: your preamp is non-linear like this:
f(x) = x + a*x*x (a is a constant, and very small in very low-distortion devices)
It will have supposedly pleasant-sounding 2nd order distortion.
Your amp is also a bit non-linear in the 2nd order distortion way:
g(x) = x + b*x*x (b is another constant similar to a)
What happens when you play music through this system?
s(x) = g(f(x))
Working through all the math, you get:
s(x) = x + b*x*x + 2*a*b*x*x*x + a*a*b*x*x*x*x
Basically, you get extra 2nd, 3rd, and 4th order components presented to your loudspeaker. Your loudspeaker then adds its own specialness and produces even more distortion components.
And this is just non-linearity, and just the tip of the iceberg of what could go wrong. There are lots of other things, and they tend to be specific to the domain of the device in which they occur, eg. resonances in speakers, software bugs in DACs, etc., all of which can show up in these measurements, but may be very difficult to trace back to the root cause.
