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I'm at a conference on applications of precision measurement to tests of physics beyond the standard model, and one of the pervasive themes is noise analysis. Unfortunately, my familiarity with this subject is minimal. Does anyone know a good reference on this matter?

I know "The Art of Electronics" has some discussion of noise, but that book tends to avoid mathematical details. I would prefer a more formal treatment---one that does not shy away from e.g. complex analysis and Fourier analysis. Also, I am looking for a holistic approach to the subject, covering various types of noise (e.g. white noise, 1/f noise, shot noise, etc.).

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  • $\begingroup$ Unless you are building pre-amplifiers for nuclear and high energy physics detectors, noise is of no concern in standard model physics. I don't know what you mean by "holistic approach". There are many more types of noise than the ones you mention there and in general one can't even use a noise approach to measurement errors but one has to use a much broader stochastic measure/hypothesis testing based view of systems with statistical errors. What you are asking is a very naive take on these things that is "just not so". $\endgroup$ – CuriousOne Jun 16 '16 at 23:22
  • $\begingroup$ @CuriousOne Noise is important for measurements of: precision electric dipole moments (see work by Gerry Gabrielse); searches for light dark matter (see work by Peter Graham); atom interferometric searches for e.g. Chameleon fields (see work by Holger Muller); 5th force searches using torsion pendulums (see work by Eot Wash group at U. Washington); gravitational wave detection (e.g. LISA/LIGO). I am not asking about measurement errors, I am asking about characterization of noise. Noise is a real issue for precision tests of BSM physics now. $\endgroup$ – Yly Jun 17 '16 at 0:07
  • $\begingroup$ @CuriousOne And by holistic, I just mean "not restricted to one particular type of noise", which is what most of the stuff on Amazon seems to do. $\endgroup$ – Yly Jun 17 '16 at 0:11
  • $\begingroup$ All of that is experiment dependent and has nothing to do with the standard model. Like I said, if you are doing pre-amplifier designs (and I should have added "and such"), then noise is important to you. Other than that you have to learn to deal with much more complex statistical errors in your experiments. Noise is the trivial part. So what are you asking? How to deal with noise, per se, or are you asking how to test hypotheses in non-trivial science experiments? The two are not the same. $\endgroup$ – CuriousOne Jun 17 '16 at 0:11
  • $\begingroup$ Most treatments of noise restrict themselves to Gaussian noise because it's comparatively easy and there are a large number of individuals, physicists and even more so EE who have to deal with it. But that is the tip of the iceberg. My feeling is that what you are really asking is how we are dealing with complex statistical errors, and you are right, that will not be handled by the noise literature. You certainly can't treat experimental errors in e.g. LIGO or experiments like ATLAS like noise. $\endgroup$ – CuriousOne Jun 17 '16 at 0:13
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I'll try to give a "holistic" answer for what concerns the importance of noise in precision measurements, with some specific references. I'll also try to address some special topics, which are not usually covered in common texts, but which are of fundamental importance in precision measurements.

Temporary disclaimer: it will take some time to complete this answer, I hope you will forgive me. In some sense, this is a very personal answer which strictly reflects some twenty years of wandering through noise in measurements.

First and foremost, noise in all measurements constitutes a fundamental limit to the measurement resolution because it masks the variations of the measurand (the quantity subject to measurement).

We can divide this important topic in several subtopics, each of which is typically addressed by different books and papers.

Mathematical modelling of noise

Noise is modelled as a stochastic process, and this subtopic is usually addressed by books on stochastic processes. In choosing these books, it's important to take into account two aspects:

  • A fundamental tool in the characterization of stochastic processes is the spectral density function: the chosen books should then have a substantial part dedicated to this tool.
  • Many basic books on stochastic processes limit their treatment to wide-sense stationary processes. Unfortunately, many noise processes which are of fundamental importance in precision measurements, like flicker noise and random walk, cannot be modelled as wide-sense stationary processes. We want, then, also books that treat non stationary stochastic processes.

One of the most comprehensive, and readable, book on stochastic processes is

[1] A. M. Yaglom, Correlation theory of stationary and random functions, vol. I; Basic results, vol. II, Supplementary notes and references, Springer Series in Statistics, Springer-Verlag, 1987.

For its style and wide choice of topics, this is a fantastic book (here, a review). Unfortunately, as far as I know, it's no longer available on the market. A (very) shortened version is

[2] A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions, Dover, 1962.

The basic theory of stochastic processes is recalled also in the following book (chaps. 1-5), which is mostly devoted to spectral analysis:

[3] D. B. Percival, and A. T. Walden. Spectral Analysis for Physical Applications, Cambridge University Press, Cambridge, 1993.

From the same authors, the following books contains a readable introduction to non-stationary processes (§7.6-7.8):

[4] D. B. Percival, and A. T. Walden. Wavelet Methods for Time Series Analysis, Cambridge University Press, Cambridge, 1993.

Noise analysis of linear systems

Noise models of devices

Noise statistics

Noise measurements

Further readings

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