# What is a complex helical sequence?

Matlab says

x = hilbert(xr) returns a complex helical sequence, sometimes called the analytic signal, from a real data sequence.

How did the name complex helical come about? How is it related to analytic signal?

From a mathematical point of view, all signals can be decomposed into complex sinusoids (sine waves), which are terms of the form $A(x) = e^{(\omega x +\phi)i}$. This is an often useful perspective. As $x$ is varied, $A(x)$ describes a circle in the complex plane; plotted in three dimensions, it is the helix from above.
(Technically, the sense of rotation is considered the sign of the frequency $\omega$, and an analytic signal only contains sinusoids with non-negative frequency.)