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I am a computer scientist who has started doing some work in the electrical engineering space – in particular, photonics. While reading about interferometric systems, I have noticed that there seems to be a focus on ensuring that the detection signal (obtained using a laser of some kind) is linear. I have not yet studied signal processing (although, I have studied quite a lot of mathematics – just not in the context of electrical engineering), so the importance of ensuring that a signal is linear (for signal processing) is not clear to me. I'm assuming that this focus on obtaining a linear signal is universal to signal processing? What is the importance of obtaining a linear signal? (In mathematics, we like linearity as a property because it makes things much simpler, but I'm more-so looking for a signal processing perspective.)

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    $\begingroup$ Please provide a reference to your claim. Linearity is a property of a system but rarely used in the context of a signal. How exactly do you define a "linear signal" ? $\endgroup$
    – Hilmar
    Jun 18, 2021 at 13:48
  • $\begingroup$ Wondering if you mean that your signals are are linear in the information of interest to interferometry? As others have said, signals are not linear, the systems that produce them are. $\endgroup$
    – Peter K.
    Jun 18, 2021 at 15:39

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Not sure what you mean by linear signal, so I will assume you are talking about the output of linear systems, which has the convenient property that the superposition of signals through the system is simply additive, and does not require the often expensive characterization or computation (if even tractable) of non-linear functions or interactions.

The amount of non-linearity in a system can also generate higher harmonics, which can vastly expand the frequency range that needs to be instrumented, filtered, or analyzed, etc.

Or it can be considered a cost issue, as in the amount of time and chalk required for the professor to write some closed form solution (etc.) to some given system’s behavior on the classroom chalkboard.

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  • $\begingroup$ I am referring to the detected signal itself, which, as I understand it, is indeed the output of the system, right? From what I've read, it seems to me that linearity in these systems (in electrical engineering, at least) is often on a spectrum (from more linear to more nonlinear), right? Or am I mistaken? So, responding directly to what you said, [...] $\endgroup$ Jun 18, 2021 at 11:45
  • $\begingroup$ [...] these systems that I am alluding to don't necessarily seem to be linear systems, but, rather, systems where there exists some degree of nonlinearity. For instance, in the case where there is a bit of nonlinearity but the signal is mostly linear, it seems to me that it is said that the signal is approximately linear (or can be considered linear for practical purposes), right? I have also seen devices such as en.wikipedia.org/wiki/Square-law_detector mentioned. $\endgroup$ Jun 18, 2021 at 11:59
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    $\begingroup$ @ThePointer a signal isn't linear. A system can be. $\endgroup$ Jun 18, 2021 at 15:29
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    $\begingroup$ (If you'd like to contradict, that's fine, but then we'll need you to define that term, linear signal, mathematically; it's certainly not something that is commonly used, and it makes little sense – something that is "linear" maps an input to an output linearly, and a signal doesn't "map"). $\endgroup$ Jun 18, 2021 at 15:35
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    $\begingroup$ Agreed @MarcusMüller: the context of the term linear signal needs to be defined before we can answer this with any authority. $\endgroup$
    – Peter K.
    Jun 18, 2021 at 15:40
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I guess that linearity is popular in signal processing for much the same reasons as in mathematics. «Linear, time-invariant» tends to be one of the first terms explained in a dsp book. Many of the tools of the trade are developed for linear systems, or quickly become impractical if you allow for nonlinearity.

If you measure some physical quantity with a linear sensor, you can often characterize it using simply its impulse response within the bounds of noise (system or measurement) and strong-signal-nonlinearity (ie clipping). You can apply deconvolution to (partially) invert a system. You can avoid having to calibrate absolute levels, rather doing a «floating» amplitude approach - when looking at numbers in a camera raw file, it is assumed that they represent the amount of light present on the sensor, but often one s does not care if it is 100 photons or 1000. You can use simple adaptive filters. Superposition is valid.

I would say that (at least within some) engineering branches, LTI is so commonly assumed that it has become an internalized view of the problems and solutions, rather than considering the complexity of nonlinearity and/or time variance.

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