Problem 1
We are given a time-invariant and linear system of which we know that the input \(u(t)\) yields an output \(y(t)\), where $$ u(t)=\left\\{\begin{array}{ll} 1 & 0 \leq t<2 \\ 0 & \text { otherwise } \end{array}, y(t)= \begin{cases}t & 0 \leq t<2 \\ 4-t & 2 \leq t<4 \\ 0 & \text { otherwise }\end{cases}\right. $$ Determine the output function \(\tilde{y}(t)\) which corresponds to the input \(\tilde{u}(t)\), where $$ \tilde{u}(t)= \begin{cases}1 & 0 \leq t<1 \\ 0 & \text { otherwise }\end{cases} $$ 147
Problem 4
Give a state space form description of a discrete-time system where \(U=Y=\\{0,1\\}\), such that the output \(y\) at time \(t\) equals 1 if the input until (and not including) \(t\) has shown an even number of 1 's and equals 0 otherwise.
