Compressing and shifting a discrete-time signal

Question

If you have a plot of a discrete time signal, say $x[n]$, and you want to change it to $x[4n+1]$, do you need to compress it before shifting it or does it not make a difference?

Answer 1

Assuming that you hold the origin fixed while compressing, it does. If you compress first, you’ll get $x[4n+1]$. If you shift first, you’ll get $x[4(n+1)]=x[4n+4]$.