Given the following difference equation,

$y(n)=0\mathrm{.}5x(n)+0\mathrm{.}5x(n-1),$

a$.$ find the $H(z)$;

b$.$ determine the impulse response $y(n)$ if the input is $x(n)=4(n)$;

c$.$ determine the step response $y(n)$ if the input is $x(n)=10u(n).$

d$.$ Plot the magnitude and phase spectrum

d$.$ Develop convolution of sum equation from the difference equation.