I have a signal $$x[n] = n(u[n] - u[n-7])$$ So it is a discrete signal that goes from 0 to 6 when $n$ goes from 0 to 6, then it is 0 for all other $n$.
I want to figure out what $x[4n+3]$ will look like.
I think I need to shift the signal by 3 to the left, so that it will equal 0 to 6, from n=-3 to n=3. Then compress the signal by 4, so that the only remaining non-zero value is at n=0.
So I think then
$x[4n+3] = 2\delta[n]$ ?
There's a good chance I did this wrong, so would any one mind checking this for me?
In case if you couldn't catch the hint in the comment,
$$x[4n+3]$$can only be nonzero at $$4n+3=0\,\Rightarrow \color{red}{n=\frac{-3}{4}},$$ $$4n+3=1\,\Rightarrow \color{red}{n=\frac{-1}{2}},$$ $$4n+3=2\,\Rightarrow \color{red}{n=\frac{-1}{4}},$$ $$4n+3=3\,\Rightarrow \color{green}{n=0},$$ $$4n+3=4\,\Rightarrow \color{red}{n=\frac{1}{4}},$$$$4n+3=5\,\Rightarrow \color{red}{n=\frac{1}{2}},$$ $$4n+3=6\,\Rightarrow \color{red}{n=\frac{3}{4}},$$
You can see that only when $n=0$, the value of $4n+3$ is an integer. For this value of $n$ we have $x[4n+3]=x[3]=3$. That is why we have $$\boxed{x[4n+3]=3\delta[n]}$$