The commonly used chirp signal in papers is a complex signal. What formula is used to generate the real signal for the chirp() function in Matlab?

In most academic papers, the formula for the linear chirp signal used is shown in the figure below. It is obvious that this is a complex signal

If I generate the signal based on this formula, the result is also a complex signal.

1.Now I am curious about what formula or method the chirp function in Matlab is based on to generate real signals？

2.Is there any connection between generating chirp signals using the formula in the figure and generating real signals using the chirp function in Matlab?

I am a beginner in signal processing .Hope someone can help me.

Answer 1

[Mathieu NOE]

hello

yes this is the general scientific definition of a chirp signal

In signal processing applications, most of the time you only need the real part of the signal , so it would become

y(t) = a(t)*cos(phi(t) + phi0) , phi is the angle at time t , and a the amplitude vs t (can also vary), phi0 the initial angle value.

matlab chirp function simply allows you to use some typical frequency profiles (linear, quadratic, log, etc...) - read the doc !

but you can also built your own function, simply create phi vs t and you are done

see home made examples attached !