This question is about combining 2 sinusoids with frequencies $\omega_1$ and $\omega_2$ into 1 "wave shape", where the frequency linearly changes from $\omega_1$ to $\omega_2$, and where the wave starts at phase = 0 radians (point A in the image), and ends back at the completion of the at $2\pi$ radians (point E), resulting in a shape similar to this, assuming $\omega_1$ is a lot smaller (larger period) than $\omega_2$:
Note that the amplitude is the same for both waves: points B and D are at equal distance from the $x$-axis.
- Is there a closed-form definition for this, like linear frequency modulation?
- Part of my question is also: where does point C end up on the x-axis if the "wave" starts at the origin (0,0)?
I was thinking about something like this:
w1: frequency 1
w2: frequency 2
t: a vector going from
T: some arbitrary number: this is part of the question I suppose..