# How to express time delayed discrete signals

Hi sorry this question might sound silly but,

a signal $$x[n]=[ 6 \: 4\: 0\: 2]$$ what is $$x[n-2]$$ then?

• why is the six bold? – Marcus Müller Feb 8 '20 at 20:20
• Typically: [0 0 6 4 0 2] – Hilmar Feb 8 '20 at 23:35
• the 6 is bold because its the first value of the signal ie x[0]. – J Leo Feb 9 '20 at 22:50
• Not silly. A potential for confusion for the beginners who make mistakes shifting the origin to $x[n]=[6\;4\;\textbf{0}\; 2]$ – jomegaA Feb 10 '20 at 9:30

The problem with representing a discrete time just as a list like: $$x[n]=[6, 4, 0, 2]$$ is that you don't have a time reference.
The first index $$n=0$$ or the sample in $$\textbf{bold}$$ or $$\underline{\mathrm{underline}}$$ is usually taken as the start of the sequence.
For example, $$x[n]=[\mathbf{6}, 4, 0, 2]$$ or $$x[n]=[\underline{6}, 4, 0, 2]$$
So $$x[n-2]$$ is a delay of two samples, and $$x[0]$$ now happens two samples later: $$x[n]=[\underline{0}, 0, 6, 4, 0, 2]$$