Consider a discrete time LTI system with the following impulse response: $h[n]=(\frac{1}{2}{)}^{n}u[n]+\frac{1}{2}(\frac{1}{4}{)}^{n}u[n].$

a$)$ Determine the difference equation relating the input $x[n]$ and the output $y[n]$ of that system. $(/10)$

b$)$ Determine the output $y[n]$ of the system if the input is $x[n]=[n]+[n-5]*(15)$

Use discrete time fourier transform to solve please