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x(t) -> analog signal

1) Sample x(t) to get x(n)

Now x(n) is modelled by a non-causal AR process say
x(n) = a*x(n-1) + a*x(n+1) + W1(n)

PSD of x(n) is  VAR(of W1)/(1-2*a*cos(w))

2) Let y(t) = x(scale*t)  ---> a scaled version of x(t), scale is not
restricted to be an integer. It is a real number.

Now sample y(t) to get y(n). And y(n) is modelled by an AR process say
y(n) = b*(y(n-1)+y(n+1)) + W2(n)

PSD of y(n) is VAR(of W2)/(1-2*b*cos(w))

My questions:

a) Is there a relationship between the parameters 'a' and 'b' ?
b) Is there a relationship between the PSD's of x(n) and y(n) ?

Although I have used here a first order process, I am interested in higher
order processes.

Any references or pointers appreciated.
Thanks

Please reply directly to : 

patel@CVLSUN1.ece.drexel.edu