A discrete$-$time system has a finite$-$duration impulse response that consists of the samples $\{1,3,-1,2\},$ commencing at n $=0.$ Explain how time$-$domain convolution can be used to calculate the system output, and calculate the response of the system to a finite$-$duration input signal that consists of the samples $\{-2,-1,1,4,3\},$ also commencing at n $=0.$ Indicate in detail the calculations needed to determine y$(3).$ State what the output would be if the same signal was input to the filter, but delayed by $2$ sample periods.