Problem$1$:

A system is described by the following Difference Equation$($DE$)$ :

$y(n)=y(n-1)+x(n)$

a$)$ Find its impulse response $($hint let $x(n)=(n)).$

b$)$ Is this system an FIR$($ Finite Inpulse Response$)$ or an IIR$($infinite Inpulse Response$)$ and why?

c$)$ Find the system Z$-$transfer function $H(z)$

Problem$2$:

A system is described by the following Difference Equation$($DE$)$ :

$y(n)=y(n-1)+\frac{1}{M}[x(n)+x(n-(M-1))]$

a$)$ Find its impulse response $($hint let $x(n)=(n))$

b$)$ Is this system an FIR$($ Finite Inpulse Response$)$ or an IIR$($infinite Inpulse Response$)$ and why?

c$)$ Find the system Z$-$transfer function $H(z)$

Problem$3$:

A system is described by the following Z$-$transfer function :

$H(z)=\frac{z}{z-1}$

a$)$ Find its Difference Equation$($DE$).$

Problem$4$:

A system is described by the following Z$-$transfer function :

$H(z)=\frac{Y(z)}{x(z)}=\frac{1}{M}\frac{[1+z^{-(M-1)}]}{(1-z^{-1})}$

a$)$ Find its Difference Equation$($DE$).$