(1) Determine whether the following signals are periodic or not . If periodic, specify the fundamental period and-frequency in Hz. a) x(t)=cos^2(2pi t) b) x(t)=cos(t)+sin(2pi t) C) x(t)=e^sint

To determine whether a signal is periodic or not, we need to check if there exists a positive constant T, called the period, such that the signal repeats itself every T units of time. If such a T exists, then the signal is periodic.<br /><br />a) For the signal $x(t) = \cos^2(2\pi t)$, we can rewrite it as $x(t) = \frac{1 + \cos(4\pi t)}{2}$. We can see that the signal is a shifted and scaled version of the cosine function with a frequency of 2 Hz. Therefore, the signal is periodic with a fundamental period of 0.5 seconds and a frequency of 2 Hz.<br /><br />b) For the signal $x(t) = \cos(t) + \sin(2\pi t)$, we can see that the first term, $\cos(t)$, is a cosine function with a frequency of 1 Hz, while the second term, $\sin(2\pi t)$, is a sine function with a frequency of 2 Hz. Therefore, the signal is periodic with a fundamental period of 2π seconds and a frequency of 1 Hz.<br /><br />c) For the signal $x(t) = e^{\sin(t)}$, we can see that the signal is a shifted and scaled version of the exponential function with a frequency of 1 Hz. Therefore, the signal is periodic with a fundamental period ofπ seconds and a frequency of 1/2π Hz.