LTI Image Interpretation

[laurita]

How would you interpretate this image about LTI systems and convolution?
If you don't get it, please go through step-by-step telling what you thinks it means...

 

[Aluvus]

h[n] is the impulse response, X[n] is the input signal, h[X0]..h[X3] is the response to each individual pulse in X[n], Y[n] is the sum of those responses, the output signal.

 

[laurita]

Do you think everything in the image is clear and correct? Is it easy to understand what you have to multiply and add together? (y[0]=..., y[1]=..., etc) What would happen if you change 'Y[3]' to 'X[1]h[2] + X[2]h[1] + X[3]h[0]'?