finding power spectral density from a vector

I have been given a vector:
begin{equation}
v= :begin{pmatrix}frac{1}{sqrt{2}}&frac{1}{sqrt{2}}end{pmatrix}
end{equation}
my job is to find the power spectral density from this vector
begin{equation}
left|Phi :_{vv}left(e^{jw}right)right|^2
end{equation}

Can somebody please direct me in the right direction to get started on solving this problem?
I know I am supposed to use the Z transform, then evaluate the Z transform at the unit circle hence the term begin{equation}e^{jomega }end{equation}
but this is a vector and there’s no dependence on a discrete time index.
Looking forward for your help. Any simple and convenient help is appreciated. Thank you very much in advance.

Update 1:
If,
begin{equation}
vleft(nright)::=:frac{1}{sqrt{2}}xleft(nright)+frac{1}{sqrt{2}}xleft(n-1right)
end{equation}
then:
begin{equation}
Vleft(e^{jomega }right):=:frac{1}{sqrt{2}}Xleft(e^{jomega :}right)+frac{1}{sqrt{2}}e^{jomega ::}Xleft(e^{jomega ::}right)
end{equation}
therefore:
begin{equation}
frac{Vleft(e^{jomega }right)}{Xleft(e^{jomega }right)}:=:Hleft(e^{jomega }right)=frac{1}{sqrt{2}}+frac{1}{sqrt{2}}e^{jomega :::}
end{equation}
How to prove the response is a low pass filter response?