(Solved): please show detailed solution for the problems shown will upvote 7.1 Use the superposition and ...

please show detailed solution

for the problems shown will upvote

7.1 Use the superposition and time-delay properties to find the $z$-transforms of the following signals $\begin{array}{rl}{x}_1[n]& =\delta [n]\\ x_2[n]& =\delta [n-1]\\ x_3[n]& =\delta [n-7]\\ x_4[n]& =2\delta [n]-3\delta [n-1]+4\delta [n-3]\end{array}$ 2 Use the superposition and time-delay properties of (7.3.1) and (7.3.4) to determine the $z$-transform $Y(z)$ in terms of $X(z)$ if $y[n]=x[n]-x[n-1]$ and in the process show that for the first difference system, $H(z)=1-z^{-1}$.