(Solved): 12 Points Determine and explain if the following systems are linear and time invariant, where \( x( ...

12 Points Determine and explain if the following systems are linear and time invariant, where \( x(t), y(t) \) are the input and output signals respectively. 1) \( y(t)=\frac{3 t d x(t)}{d t} \) 2) \( y(t)=\cos (2 \pi t) x(t) \) 3) \( y(t)=t^{2} x(t) \) 4) \( y(t)=x(t)+2 x(t-1)+3 x(t-2) \) Q2 10 Points Find the Trigonometric Fourier series for the square \( 2 \pi \)-periodic wave defined on the interval \( [-\pi, \pi] \) : \[ f(t)=\left\{\begin{array}{ll} 0, & \text { if }-\pi \leq t \leq 0 \\ 1, & \text { if } \quad 0