Hello all,
I have a question on z-transforms.the question states
"determine the casual signal x(n) having the z-transform
X(z) = 1/(1-2z^-1)(1 - z^-1)^2.
if i solve this by rewriting as
X(z)/z = z^2 /(z-2)(z-1)^2
i get x(n) as 4(2^n) u(n) - 3u(n) - nu(n).
But if i try to find the value by writing the partial fractions for the given function as it is
(i.e) A/(1 - 2z^-1) + B/(1 - z^-1) + C /(1 - z^-1)^2
i get A,B,C as 4,-2,-1
i get x(n) as 4(2^n) - 2u(n) - n u(n)
i dont know where iam going wrong.
is it right on my part to take partial fractions as i have done in the second case and solve the given function in z-inverse as it is?
Thank you
I have a question on z-transforms.the question states
"determine the casual signal x(n) having the z-transform
X(z) = 1/(1-2z^-1)(1 - z^-1)^2.
if i solve this by rewriting as
X(z)/z = z^2 /(z-2)(z-1)^2
i get x(n) as 4(2^n) u(n) - 3u(n) - nu(n).
But if i try to find the value by writing the partial fractions for the given function as it is
(i.e) A/(1 - 2z^-1) + B/(1 - z^-1) + C /(1 - z^-1)^2
i get A,B,C as 4,-2,-1
i get x(n) as 4(2^n) - 2u(n) - n u(n)
i dont know where iam going wrong.
is it right on my part to take partial fractions as i have done in the second case and solve the given function in z-inverse as it is?
Thank you