calculate discrete time signal convolution example by hand

Question

Conv. is defined this way:$y[n] = \sum_{i=0}^\infty h[i]*x[n-i]$

I have this example: $x[n] =(3,-1,2,0,1)$ at sample times $n= (0,1,2,3,4)$ is the input of an LTI system with impulse response $h[n] = (2,3,4,1)$ at sample time $n = (0,1,2,3)$. Now I calculate it like the following: This approach was done by our teacher:

$3- 0- 0-0- 0$

$1-3-0-0-0$

$2-(-1)-3-0-0$

$0-2-(-1)-3-0$

$1-0-2-(-1)-3$

$0-1-0-2-(-1)$

$0-0-1-0-2$

$0-0-0-1-0$

$0-0-0-0-1$

Now multiply first column by 2, second column by 3, third column by 4, fourth column by 1 but what I should do with fifth column. Since there is no element left for n of the impulse response h[n]. After multiply these we would add these and get the output. Any hints to what should I do with the last column!

Thanks for the help!

Answer 1

Just assume that $x[n]$ and $h[n]$ are zero for all sample times outside those that have been specified.