I have the following sequence flow, graphically:
According to my understanding, the diagram describes the following sequence
$$ y[n] = (cx[n] + x[n-1])[n-3](-1) $$
Now I'm very tempted to simplify this further:
$$ y[n] = (cx[n-3] + x[n-4])(-1) $$
I saw something like this done before in some examples, but I wasn't able to find a justification why such a simplification would be valid. So my question:
- Is that simplification indeed valid?
- Is there a theorem or so that proves this "distributive property" (or whatever the correct name is)?