fundamental question about convolution on discrete time signals (LTI systems)

[robismyname]

I know that the impulse response "h" represents the LTI systems response to a impulse signal δ.

**************
δ * * h
------------> * Discrete LTI * --------------->
* System * y
* *
**************

Dumb question #1. Is h; the impulse response also y the output?

Dumb question #2. If h is the impulse response you get from inputting a impulse function δ into the system then how is convolution applied in obtaining h? What/where is the second signal that gets convoluted with δ?

I ask because a signals tutorial I am using has a convolution formula:
∞
h = ∑ x(j) * δ(n-j) = x * δ
-∞

and i see the impulse function gets convolved with x? so does that mean the impulse response h = impulse function δ * the impulse response h?

Please help me with clarifying this concept.

 

[iVenky]

Yep. dirac * h gives you h.

Actually the concept of impulse response is simple.
You have some system "x" and you have to find what that "x" is. You have access to its input and output but not to the system. What you do is this- You send '1' and see what its output is. Assuming that multiplication takes place instead of convolution (just assume for the time being) then the output of the system will be

1 * x = x.

Now you have found out the value of 'x'. ( Let's assume that the value of 'x' is 5)
Now whenever you give any input the output can be simply obtained by multiplying 'x' with the input.
For eg: if you send 3 as input the output will be 3 * x = 3x. (note that this time you know the value of x already) and you can simply write output = 3 * x = 3 * 5 = 15.

The same concept can be applied to a system in which convolution takes place. dirac function is similar to '1' as used in the above example. h is similar to 'x' as used in the above example.