GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 45 of 65

Marks: +1, -0

The causal signal with

z

-transform

z^{2}(z-a)^{-2}

is:

(u[n]

is the unit step signal).

Solution:

f(z)=\;{z^{2}}/{(z-a)^{2}}

a^{n} u[n] ↔ \;{z}/{(z-a)}

a^{n} u[n] ↔-z[\;{d}/{d z}(\;{z}/{z-a})]

=-z[\;{(z-a) 1-z}/{(z-a)^{2}}]

{n} . {a}^{ {n}} {u}[ {n}] ↔ \;{ {az}}/{( {z}- {a})^{2}}

{n} ⋅ {a} {n}^{-1} {u}[ {n}] ↔ \;{ {z}}/{( {z}- {a})^{2}}

(n+1) a^{n} u[n] ↔ \;{z^{2}}/{(z-a)^{2}}

Go to Question:

Prev Question

Next Question