Test: One Sided Z Transform - Electrical Engineering (EE) MCQ

Explanation: The z-transform of the x(n) whose definition exists in the range n=-∞ to +∞ is known as bilateral or two sided z-transform. But in the given question the value of n=0 to +∞. So, such a z-transform is known as Unilateral or one sided z-transform.

Explanation: One sided z-transform is unique only for causal signals, because only these signals are zero for n<0.

Explanation: Since the one sided z-transform is valid only for n>=0, the z-transform of the given signal will be X⁺(z)= 5+7z^-1+z^-3.

Explanation: Since the signal x(n)= δ(n-k) is a causal signal i.e., it is defined for n>0 and x(n)=1 at z=k
So, from the definition of one sided z-transform X⁺(z)=z^-k.

Explanation: Since the signal x(n)= δ(n+k) is an anti causal signal i.e., it is defined for n<0 and x(n)=1 at z= -k. Since the one sided z-transform is defined only for causal signal, in this case X⁺(z)=0.

Explanation: From the definition of one sided z-transform we have,

Explanation:

Explanation: We will apply the time advance theorem with the value of k=2.We obtain,

Explanation: In the above theorem, we are calculating the value of x(n) at infinity, so it is called as final value theorem.

Explanation: The step response of the system is y(n)=x(n)*h(n) where x(n)=u(n)
On applying z-transform on both sides, we get