Hi,
Using a table like that is not exactly the same as using an impulse response to get an output. All that is is a lookup table, where the values are stored in tabular form and the next value that is looked up is simply directed to the output. That's not the same as when using an impulse response as the following will show.
Say we start with a simple sine lookup table like this (the '9' and '-9' here are rounded from 8.66 and -8.66 for simplicity):
{ 0, 5, 9, 10, 9, 5, 0, -5, -9,-10, -9, -5 }
That's a table of values for sine where the peak is 10 volts. To get the next output, we simply step to the next counter value and read the table value and direct that to the output. That's not exactly the same as when we use an impulse response, although we could make it into one.
A better example is this one. Lets say that our h(n) is this instead of the sine table:
{ 5, 4, 1, -1, -4, -5, -5, -4, -1, 1, 4, 5 }
Look strange? It might look strange, but if we use a step input for x(n) guess what we get as output?
x(n)*h(n)={ 0, 5, 9, 10, 9, 5, 0, -5, -9,-10, -9, -5 }
and that's the original sine table.
So with the lookup table we simply look up values and direct them to the output, and there doesnt have to be any input. When using the impulse response, we have to convolve it with the input in order to get the output. The impulse response (or better called "unit sample response" here) could be that of a filter so that the output ends up being the input signal filtered in some way.