1D-Phase Unwrapping

I am new to signal processing and I am reading about 1D phase unwrapping Here is the paper that I am reading.

It refers to x as the signal but then it shows in the graph the axis are origina phase in radians againts sample index. So is x the signal or the phase function? Also it says that signal x whose amplitude exceeds the range [-π,π]. All the above are for figures 1. I am asking that, because I am confused on wether we compare phases or amplitudes. So is x the phase of a function like sin(x)? I think whis sums up my question (page 1 of pdf) I hope i didnt confuse anyone.

2 Answers

IMO this not a particularly well written paper with confusing terminology and needless complications, so I recommend to look somewhere else.

So is x the signal or the phase function?

It is the phase function. Choosing a sine wave as a phase function is certainly confusing, but it IS a phase function. "amplitude" here just refers to the magnitude of the phase.

So if I understand right, $$x$$ is the phase function thus a signal fas the form of $$f(x) = \sin(x)$$ which x is the phase function and can be whatever and $$f(x)$$ is the amplitude function.