Final answer:
The function x(t) is composed of two periodic signals with different angular frequencies that are not integer multiples of each other; thus, the function is not periodic and does not have a fundamental period or frequency.
Step-by-step explanation:
The question is about determining whether the given function x(t)=6e^{j6t}+je^{j9t} is periodic, and if it is, finding its fundamental period and fundamental frequency. This function is a sum of two complex exponentials, each of which represents a periodic signal with different angular frequencies. To determine if the overall signal is periodic, we look at the angular frequencies of each component and see if they are multiples of a common frequency.
The angular frequency of the first term is 6, and the angular frequency of the second term is 9. The ratio 9/6 simplifies to 3/2, which is not an integer. Therefore, the signals have angular frequencies that are not integer multiples of each other, implying that they do not have a common fundamental period, and hence the overall signal is not periodic.
For periodic signals, the fundamental period T is the inverse of the fundamental frequency f, and the fundamental frequency is the number of repetitions of the signal over a unit of time. Also, the angular frequency ω is related to the fundamental frequency by the equation ω = 2πf.