The signal $x(t)$ is made up of a sum-of-sinusoids as follows: \[ x(t)=1.2 \cos (168 \pi+0.05)-2.5 \sin (588 \pi t)+5 \cos \left(420 \pi t+\frac{\pi}{3}\right)+0.5 \cos (1092 \pi t-0.4 \pi) \] what is the fundamental frequency [fO] $\mathrm{Hz}$ of $x(t)$

Step 1 ：Given signal $x(t)$ is:

Step 2 ：\[x(t)=1.2 \cos (168 \pi+0.05)-2.5 \sin (588 \pi t)+5 \cos \left(420 \pi t+\frac{\pi}{3}\right)+0.5 \cos (1092 \pi t-0.4 \pi)\]

Step 3 ：Extract the frequencies from the signal:

Step 4 ：\[frequencies = [168, 588, 420, 1092]\]

Step 5 ：Find the greatest common divisor (GCD) of the frequencies:

Step 6 ：\[fundamental\_frequency = 42.0\]

Step 7 ：\(\boxed{The\ fundamental\ frequency\ of\ x(t)\ is\ 42\ Hz.}\)