The terms 'error' and 'noise' are often used to mean the same thing: the difference between a measured value and the real value of the input.
I'm not going to use them that way. For this tutorial, 'error' has the definition given above, and 'noise' is a specfic kind of error. Also for the purposes of this tutorial, error has two properties called repeatability and correlation.
Repeatable errors are caused by flaws in a measuring system, and are the best kind of errors to have. You can identify them, measure them, and fix them. Unrepeatable errors are caused by randomness in the universe. We can identify what's causing them, and there are ways to minimize them, but we can never eliminate them completely.
The process of measuring repeatable error is called calibration. You do it by comparing your measurement to a measurement of the same signal from another instrument you trust more. If you adjust your measurement system to eliminate calibrated errors, it's called correction. If you just subtract the calibrated error from your measurements, it's callled compensation.
Correlated errors have some kind of relationship to the thing you're measuring. You can define the error as a function of the input. Uncorrelated errors stay the same regardless of the input.
If you draw a graph of a circuit's ideal input-output function, then modify it to account for errors in the real circuit, uncorrelated errors don't change the shape of the curve. They just shift the real curve some distance away from the ideal one, so we generally call them offsets. Correlated errors do change the shape of the curve, and are generally called distortion.
Arranged by order of difficulty, the major categories of error are:
- Repeatable uncorrelated errors, or 'fixed offsets'.
These are the easiest to calibrate and correct.
- Repeatable and unrepeatable correlated errors, or 'distortion'.
Distortion is a big problem, and most forms of distortion are impossible to fully correct, but there's a huge body of engineering knowledge about compensating distortion. We know how to build circuits that minimize the effects of distortion, and we know how to move distortion to places we can ignore.
- Unrepeatable uncorrelated errors, or 'noise'.
This is the part we can never truly eliminate. We can select components that generate as little noise as possible, and there are ways to build circuits that minimize the number of noise sources. There are even ways to move noise to frequencies that can be ignored. There will always be some amount of noise that's impossible to remove though.
It's impossible to predict the noise error in any single measurement, but we can analyze noise statistically.