Question: $x[n]= 3\cos(0.3\pi n + 0.1) - \sin(0.11\pi n -\frac{\pi}{3})$ Find the fundamental period for this discrete signal.
My attempt: Write the two functions as:
$$\underbrace {3\cos\left(\frac{3}{10}\pi n + 0.1\right)}_{=f(n)} - \underbrace{\sin\left(\frac{11}{100}\pi n -\frac{\pi}{3}\right)}_{=g(n)}$$
The period of $f(n)$ is as follows:
$$T_f=\frac{2\pi}{\frac{3\pi}{10}}\cdot k$$ For $k=3$, $T_f=20$
The period of $g(n)$ is as follows:
$$T_g=\frac{2\pi}{\frac{11\pi}{100}}\cdot m$$ For $m=11$, $T_g=200$
Now since both of these discrete-time signals are periodic there sum should also be periodic but with what fundamental period?
Would it just be the $\textbf{LCM}$ of $T_f$ and $T_g$?