For Programming #2, by "pencil-and-paper" we mean using Matlab.
In Matlab, when you have got a string of expression, how to put an array input and get the array output?
Here is the trick by following example
Note: x and impulse_response are all symbolic strings; t is the numerical array,
"hh" is also an numerical array.
So, the magic is the "subs". To know more on "subs", type "help subs"
HTH. YangQuan Chen