Interpret convolution diagram

Question

How do I interpret this "do convolutions" diagram?

1) How are the results computed?

2) When looking at this part: "x[n-k]" Do you interpret convolutions as delays or time reversals?

$ y[n]= \sum_{k=0}^{M} h[k]x[n-k] = h[n]*x[n]$

$ h[n] = \delta[x] - \delta[n-1] + 2\delta[n-2] - \delta[n-3]+ \delta[n-4] $

Answer 1

1. Convolutions are computed by adding up the values of $h[k]x[n-k]$, which makes sense following the formula $$h*x=\sum_{k=0}^nh[k]x[n-k]$$ Along these lines, note that each entry for $y[n]$ is the sum of the entries above (not including the top two rows).
2. $x[n-k]$ is a time delay, not a time reversal (which would be something along the lines $x[-n]$). If you think of $x[n-k]$ as a function of $k$, then $x$ is first time reversed, then shifted forward by $n$.